42:@0.058599:0.966558:0.074760:0.966558:0.074760:0.950778:0.058599:0.950778:0.000000:0.000000 Operaciones con funciones reales:@0.404235:0.122221:0.805588:0.122221:0.805588:0.077562:0.404235:0.077562:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 M.5.1.25. Realizar las operaciones de adición y producto entre funciones reales, y el producto de números reales por funciones reales, aplicando propiedades de los números reales.:@0.148948:0.939630:0.886004:0.939630:0.886004:0.929588:0.148948:0.929588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean :@0.404236:0.159137:0.478330:0.159137:0.478330:0.142640:0.404236:0.142640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.442381:0.159253:0.453652:0.159253:0.453652:0.142784:0.442381:0.142784:0.000000 :@0.458140:0.158920:0.474188:0.158920:0.474188:0.144273:0.458140:0.144273:0.000000 R :@0.478677:0.158168:0.497403:0.158168:0.497403:0.144722:0.478677:0.144722:0.000000:0.000000 con Ø Denotamos con :@0.497808:0.159137:0.709030:0.159137:0.709030:0.142640:0.497808:0.142640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.529248:0.159253:0.540519:0.159253:0.540519:0.142784:0.529248:0.142784:0.000000 ≠ . :@0.545007:0.158631:0.588647:0.158631:0.588647:0.140919:0.545007:0.140919:0.000000:0.000000:0.000000:0.000000:0.000000 F(A) :@0.709377:0.159253:0.743206:0.159253:0.743206:0.142784:0.709377:0.142784:0.000000:0.000000:0.000000:0.000000:0.000000 el conjunto de todas :@0.743555:0.159137:0.895866:0.159137:0.895866:0.142640:0.743555:0.142640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las funciones reales definidas en Si :@0.404198:0.176488:0.670316:0.176488:0.670316:0.159990:0.404198:0.159990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A.:@0.635400:0.176604:0.649907:0.176604:0.649907:0.160135:0.635400:0.160135:0.000000:0.000000 f :@0.670636:0.176604:0.679074:0.176604:0.679074:0.160135:0.670636:0.160135:0.000000:0.000000 :@0.679383:0.176271:0.695431:0.176271:0.695431:0.161624:0.679383:0.161624:0.000000 :@0.695431:0.176488:0.699573:0.176488:0.699573:0.159990:0.695431:0.159990:0.000000 F(A), :@0.699881:0.176604:0.736562:0.176604:0.736562:0.160135:0.699881:0.160135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se debe entender que :@0.736870:0.176488:0.895851:0.176488:0.895851:0.159990:0.736870:0.159990:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dom(f) = A, :@0.404178:0.193954:0.494087:0.193954:0.494087:0.177486:0.404178:0.177486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para cada :@0.494087:0.193839:0.567159:0.193839:0.567159:0.177341:0.494087:0.177341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.567159:0.193954:0.578776:0.193954:0.578776:0.177486:0.567159:0.177486:0.000000:0.000000  :@0.578776:0.193622:0.599640:0.193622:0.599640:0.178975:0.578776:0.178975:0.000000:0.000000 A, f(x) :@0.599640:0.193954:0.645067:0.193954:0.645067:0.177486:0.599640:0.177486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.645067:0.193622:0.665932:0.193622:0.665932:0.178975:0.645067:0.178975:0.000000:0.000000 R :@0.665932:0.192870:0.684657:0.192870:0.684657:0.179423:0.665932:0.179423:0.000000:0.000000 y :@0.684657:0.193839:0.696621:0.193839:0.696621:0.177341:0.684657:0.177341:0.000000:0.000000 Rec(f) :@0.696621:0.193954:0.761659:0.193954:0.761659:0.177486:0.696621:0.177486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.741469:0.193622:0.757517:0.193622:0.757517:0.178975:0.741469:0.178975:0.000000 R:@0.761659:0.192870:0.775568:0.192870:0.775568:0.179423:0.761659:0.179423:0.000000 . :@0.775568:0.193839:0.782465:0.193839:0.782465:0.177341:0.775568:0.177341:0.000000:0.000000 Sean :@0.404178:0.228540:0.441977:0.228540:0.441977:0.212043:0.404178:0.212043:0.000000:0.000000:0.000000:0.000000:0.000000 f, g :@0.441495:0.228656:0.463303:0.228656:0.463303:0.212187:0.441495:0.212187:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.462822:0.228323:0.483686:0.228323:0.483686:0.213676:0.462822:0.213676:0.000000:0.000000 F(A).:@0.483127:0.228656:0.515666:0.228656:0.515666:0.212187:0.483127:0.212187:0.000000:0.000000:0.000000:0.000000:0.000000 Recuerda que y son iguales, :@0.515666:0.228540:0.734458:0.228540:0.734458:0.212043:0.515666:0.212043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f g:@0.619851:0.228656:0.646726:0.228656:0.646726:0.212187:0.619851:0.212187:0.000000:0.000000:0.000000 f = g:@0.733976:0.228656:0.763899:0.228656:0.763899:0.212187:0.733976:0.212187:0.000000:0.000000:0.000000:0.000000:0.000000 , si y solo si se veri-:@0.763899:0.228540:0.891743:0.228540:0.891743:0.212043:0.763899:0.212043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fica :@0.404198:0.245891:0.433346:0.245891:0.433346:0.229393:0.404198:0.229393:0.000000:0.000000:0.000000:0.000000:0.000000 f(x) = g(x) , x A.:@0.432903:0.246007:0.573254:0.246020:0.573254:0.229552:0.432903:0.229538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.539000:0.246310:0.555048:0.246310:0.555048:0.231663:0.539000:0.231663:0.000000 La función :@0.573254:0.245905:0.655994:0.245905:0.655994:0.229407:0.573254:0.229407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f F(A),:@0.655551:0.246020:0.720562:0.247265:0.720562:0.230796:0.655551:0.229552:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.659871:0.249235:0.664577:0.249235:0.664577:0.239634:0.659871:0.239634:0.000000 :@0.668276:0.245674:0.684324:0.245674:0.684324:0.231027:0.668276:0.231027:0.000000 definida como :@0.720562:0.245891:0.831913:0.245891:0.831913:0.229393:0.720562:0.229393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f (x) = 0, :@0.831470:0.246007:0.895912:0.246007:0.895912:0.229538:0.831470:0.229538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0:@0.835800:0.249235:0.840506:0.249235:0.840506:0.239634:0.835800:0.239634:0.000000 :@0.891751:0.246007:0.895893:0.246007:0.895893:0.229538:0.891751:0.229538:0.000000 x A, :@0.414720:0.264615:0.465176:0.264615:0.465176:0.248146:0.414720:0.248146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.426337:0.263024:0.442385:0.263024:0.442385:0.248377:0.426337:0.248377:0.000000 se denomina función cero o función nula.:@0.465176:0.263241:0.761799:0.263241:0.761799:0.246743:0.465176:0.246743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Adición:@0.404236:0.299341:0.467138:0.299341:0.467138:0.281658:0.404236:0.281658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Definición:@0.404236:0.316511:0.484320:0.316511:0.484320:0.299565:0.404236:0.299565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sean :@0.484322:0.316048:0.529075:0.316048:0.529075:0.299551:0.484322:0.299551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g :@0.529133:0.316164:0.555680:0.316164:0.555680:0.299695:0.529133:0.299695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.555738:0.315831:0.576602:0.315831:0.576602:0.301185:0.555738:0.301185:0.000000:0.000000 F(A). :@0.576622:0.316164:0.613303:0.316164:0.613303:0.299695:0.576622:0.299695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La suma de con se nota :@0.613361:0.316048:0.805955:0.316048:0.805955:0.299551:0.613361:0.299551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.698397:0.316164:0.702694:0.316164:0.702694:0.299695:0.698397:0.299695:0.000000 g:@0.738045:0.316164:0.745482:0.316164:0.745482:0.299695:0.738045:0.299695:0.000000 f + g:@0.806013:0.316164:0.841153:0.316164:0.841153:0.299695:0.806013:0.299695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y es la :@0.841153:0.316048:0.895941:0.316048:0.895941:0.299551:0.841153:0.299551:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función real definida en como: :@0.404236:0.333399:0.640484:0.333399:0.640484:0.316901:0.404236:0.316901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.576389:0.333515:0.587659:0.333515:0.587659:0.317046:0.576389:0.317046:0.000000 (f + g)(x) = f(x) + g(x), x :@0.536126:0.350866:0.724507:0.350865:0.724507:0.334396:0.536126:0.334397:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.724507:0.350532:0.745371:0.350532:0.745371:0.335885:0.724507:0.335885:0.000000:0.000000 A.:@0.745371:0.350865:0.759878:0.350865:0.759878:0.334396:0.745371:0.334396:0.000000:0.000000 :@0.404241:0.368100:0.408383:0.368100:0.408383:0.351602:0.404241:0.351602:0.000000 La operación adición “ ” en :@0.404241:0.385451:0.594909:0.385451:0.594909:0.368953:0.404241:0.368953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.554452:0.386824:0.565337:0.386824:0.565337:0.370356:0.554452:0.370356:0.000000 F(A) :@0.594524:0.385566:0.626813:0.385566:0.626813:0.369098:0.594524:0.369098:0.000000:0.000000:0.000000:0.000000:0.000000 es la función que se define como sigue: :@0.626427:0.385451:0.892979:0.385451:0.892979:0.368953:0.626427:0.368953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 + ::@0.564913:0.419531:0.582792:0.419531:0.582792:0.403062:0.564913:0.403062:0.000000:0.000000:0.000000 F(A) x F(A) F(A) :@0.582792:0.410725:0.735161:0.410725:0.735161:0.394256:0.582792:0.394256:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 →:@0.681044:0.418708:0.697189:0.418708:0.697189:0.398846:0.681044:0.398846:0.000000 :@0.564913:0.428076:0.569055:0.428076:0.569055:0.411607:0.564913:0.411607:0.000000 (f, g) f + g.:@0.601768:0.428076:0.689733:0.428076:0.689733:0.411607:0.601768:0.411607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ↦:@0.634923:0.436059:0.651723:0.436059:0.651723:0.416196:0.634923:0.416196:0.000000 :@0.731106:0.435362:0.735248:0.435362:0.735248:0.418865:0.731106:0.418865:0.000000 Intervienen los siguientes elementos: :@0.404232:0.470064:0.661084:0.470064:0.661084:0.453566:0.404232:0.453566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f(x), g(x) :@0.661751:0.470180:0.722369:0.470180:0.722369:0.453711:0.661751:0.453711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.723448:0.469847:0.744312:0.469847:0.744312:0.455200:0.723448:0.455200:0.000000:0.000000 R :@0.745535:0.469095:0.764261:0.469095:0.764261:0.455648:0.745535:0.455648:0.000000:0.000000 y la adición “ ” en :@0.765513:0.470064:0.895891:0.470064:0.895891:0.453566:0.765513:0.453566:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.853209:0.471438:0.864094:0.471438:0.864094:0.454969:0.853209:0.454969:0.000000 R:@0.404213:0.486446:0.418122:0.486446:0.418122:0.472999:0.404213:0.472999:0.000000 , con lo que se tiene :@0.418122:0.487415:0.564324:0.487415:0.564324:0.470917:0.418122:0.470917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f(x) + g(x) :@0.564536:0.487530:0.636685:0.487530:0.636685:0.471062:0.564536:0.471062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.636897:0.487198:0.657761:0.487198:0.657761:0.472551:0.636897:0.472551:0.000000:0.000000 R :@0.658013:0.486446:0.676739:0.486446:0.676739:0.472999:0.658013:0.472999:0.000000:0.000000 que es el valor de la :@0.676989:0.487415:0.820631:0.487415:0.820631:0.470917:0.676989:0.470917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función:@0.820843:0.487632:0.877847:0.487632:0.877847:0.470917:0.820843:0.470917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o :@0.877849:0.487415:0.895881:0.487415:0.895881:0.470917:0.877849:0.470917:0.000000:0.000000:0.000000 imagen de:@0.404213:0.504765:0.478365:0.504765:0.478365:0.488268:0.404213:0.488268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f + g :@0.478365:0.504881:0.525834:0.504881:0.525834:0.488412:0.478365:0.488412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el punto :@0.525834:0.504765:0.611777:0.504765:0.611777:0.488268:0.525834:0.488268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.611777:0.504881:0.623394:0.504881:0.623394:0.488412:0.611777:0.488412:0.000000:0.000000  :@0.623394:0.504549:0.644258:0.504549:0.644258:0.489902:0.623394:0.489902:0.000000:0.000000 A.:@0.644258:0.504881:0.658765:0.504881:0.658765:0.488412:0.644258:0.488412:0.000000:0.000000 Ejercicios resueltos:@0.404213:0.539843:0.534868:0.539843:0.534868:0.523056:0.404213:0.523056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1.:@0.404213:0.557035:0.416485:0.557035:0.416485:0.540320:0.404213:0.540320:0.000000:0.000000 Sean :@0.416485:0.556818:0.465746:0.556818:0.465746:0.540320:0.416485:0.540320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A = :@0.465746:0.556933:0.496185:0.556933:0.496185:0.540465:0.465746:0.540465:0.000000:0.000000:0.000000:0.000000 [–1,1] y :@0.496281:0.556818:0.554636:0.556818:0.554636:0.540320:0.496281:0.540320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f , g :@0.538530:0.556933:0.581646:0.556933:0.581646:0.540465:0.538530:0.540465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000  :@0.581646:0.556601:0.602510:0.556601:0.602510:0.541954:0.581646:0.541954:0.000000:0.000000 F(A):@0.602510:0.556933:0.632198:0.556933:0.632198:0.540465:0.602510:0.540465:0.000000:0.000000:0.000000:0.000000 definidos como sigue: :@0.632198:0.556818:0.799322:0.556818:0.799322:0.540320:0.632198:0.540320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404213:0.574863:0.408355:0.574863:0.408355:0.558365:0.404213:0.558365:0.000000 f x:@0.430167:0.576171:0.452046:0.576171:0.452046:0.559703:0.430167:0.559703:0.000000:0.000000:0.000000 :@0.434463:0.576171:0.438605:0.576171:0.438605:0.559703:0.434463:0.559703:0.000000 ( ):@0.437078:0.577469:0.459540:0.577469:0.459540:0.556770:0.437078:0.556770:0.000000:0.000000:0.000000 =:@0.461149:0.576056:0.471957:0.576056:0.471957:0.559558:0.461149:0.559558:0.000000 :@0.471957:0.576056:0.476099:0.576056:0.476099:0.559558:0.471957:0.559558:0.000000 x:@0.475444:0.576171:0.482919:0.576171:0.482919:0.559703:0.475444:0.559703:0.000000 +:@0.482919:0.576027:0.497907:0.576027:0.497907:0.558633:0.482919:0.558633:0.000000 | | 1,:@0.499256:0.576056:0.549538:0.576056:0.549538:0.559558:0.499256:0.559558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.504265:0.576056:0.508407:0.576056:0.508407:0.559558:0.504265:0.559558:0.000000 x:@0.507116:0.576171:0.514591:0.576171:0.514591:0.559703:0.507116:0.559703:0.000000 :@0.514591:0.576171:0.518733:0.576171:0.518733:0.559703:0.514591:0.559703:0.000000 +:@0.523299:0.576027:0.538287:0.576027:0.538287:0.558633:0.523299:0.558633:0.000000 :@0.549538:0.576056:0.553680:0.576056:0.553680:0.559558:0.549538:0.559558:0.000000 g x:@0.562427:0.576171:0.584832:0.576171:0.584832:0.559703:0.562427:0.559703:0.000000:0.000000:0.000000 ( ):@0.569864:0.577469:0.592326:0.577469:0.592326:0.556770:0.569864:0.556770:0.000000:0.000000:0.000000 =:@0.593935:0.576056:0.604743:0.576056:0.604743:0.559558:0.593935:0.559558:0.000000 :@0.604743:0.576056:0.625569:0.576056:0.625569:0.559558:0.604743:0.559558:0.000000:0.000000:0.000000 x:@0.625569:0.576171:0.633044:0.576171:0.633044:0.559703:0.625569:0.559703:0.000000 :@0.633044:0.576171:0.637186:0.576171:0.637186:0.559703:0.633044:0.559703:0.000000 1:@0.650171:0.576056:0.658667:0.576056:0.658667:0.559558:0.650171:0.559558:0.000000 , :@0.658667:0.576056:0.665564:0.576056:0.665564:0.559558:0.658667:0.559558:0.000000:0.000000 x:@0.672191:0.576171:0.679666:0.576171:0.679666:0.559703:0.672191:0.559703:0.000000 :@0.679666:0.576171:0.683808:0.576171:0.683808:0.559703:0.679666:0.559703:0.000000 [ :@0.695587:0.577469:0.705759:0.577469:0.705759:0.556770:0.695587:0.556770:0.000000:0.000000 1,1 . Calculemos algunos :@0.715899:0.576056:0.895899:0.574864:0.895899:0.558366:0.715899:0.559558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ]:@0.735645:0.577469:0.741001:0.577469:0.741001:0.556770:0.735645:0.556770:0.000000 f:@0.396924:0.608863:0.401220:0.608863:0.401220:0.592394:0.396924:0.592394:0.000000 1 = 1:@0.425351:0.608744:0.476827:0.608744:0.476827:0.592247:0.425351:0.592247:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.403834:0.610157:0.383105:0.610157:0.383105:0.589458:0.403834:0.589458:0.000000 ):@0.432058:0.610157:0.411328:0.610157:0.411328:0.589458:0.432058:0.589458:0.000000 +:@0.476596:0.608715:0.491584:0.608715:0.491584:0.591321:0.476596:0.591321:0.000000 1 1=1,:@0.510160:0.608744:0.570229:0.608744:0.570229:0.592247:0.510160:0.592247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.521257:0.608715:0.536245:0.608715:0.536245:0.591321:0.521257:0.591321:0.000000 f:@0.585121:0.608860:0.589417:0.608860:0.589417:0.592391:0.585121:0.592391:0.000000 1:@0.615857:0.599747:0.624353:0.599747:0.624353:0.583249:0.615857:0.583249:0.000000 2:@0.615222:0.619946:0.623718:0.619946:0.623718:0.603449:0.615222:0.603449:0.000000 =:@0.634546:0.608744:0.645354:0.608744:0.645354:0.592247:0.634546:0.592247:0.000000 1:@0.664021:0.599747:0.672517:0.599747:0.672517:0.583249:0.664021:0.583249:0.000000 2:@0.663385:0.619946:0.671881:0.619946:0.671881:0.603449:0.663385:0.603449:0.000000 +:@0.675175:0.608712:0.690164:0.608712:0.690164:0.591317:0.675175:0.591317:0.000000 1:@0.711031:0.599747:0.719527:0.599747:0.719527:0.583249:0.711031:0.583249:0.000000 2:@0.710395:0.619946:0.718891:0.619946:0.718891:0.603449:0.710395:0.603449:0.000000 +:@0.725018:0.608712:0.740006:0.608712:0.740006:0.591317:0.725018:0.591317:0.000000 1=1,:@0.740931:0.608741:0.773990:0.608741:0.773990:0.592243:0.740931:0.592243:0.000000:0.000000:0.000000:0.000000 f:@0.365085:0.651727:0.369381:0.651727:0.369381:0.635258:0.365085:0.635258:0.000000 0 =0:@0.379900:0.651611:0.419768:0.651611:0.419768:0.635113:0.379900:0.635114:0.000000:0.000000:0.000000:0.000000 ():@0.372005:0.653024:0.396086:0.653024:0.396086:0.632325:0.372005:0.632325:0.000000:0.000000 + +:@0.421541:0.651582:0.469550:0.651582:0.469550:0.634188:0.421541:0.634188:0.000000:0.000000:0.000000 0:@0.441480:0.651611:0.449976:0.651611:0.449976:0.635113:0.441480:0.635113:0.000000 1=1,:@0.470474:0.651611:0.503533:0.651611:0.503533:0.635113:0.470474:0.635113:0.000000:0.000000:0.000000:0.000000 f:@0.518426:0.651726:0.522722:0.651726:0.522722:0.635258:0.518426:0.635258:0.000000 1:@0.534974:0.642617:0.543470:0.642617:0.543470:0.626120:0.534974:0.626120:0.000000 2:@0.534339:0.662816:0.542835:0.662816:0.542835:0.646319:0.534339:0.646319:0.000000 =:@0.553664:0.651611:0.564472:0.651611:0.564472:0.635113:0.553664:0.635113:0.000000 1:@0.568942:0.642617:0.577438:0.642617:0.577438:0.626120:0.568942:0.626120:0.000000 2:@0.568306:0.662816:0.576802:0.662816:0.576802:0.646319:0.568306:0.646319:0.000000 +:@0.580096:0.651582:0.595085:0.651582:0.595085:0.634188:0.580096:0.634188:0.000000 1:@0.601770:0.642617:0.610266:0.642617:0.610266:0.626120:0.601770:0.626120:0.000000 2:@0.601134:0.662816:0.609630:0.662816:0.609630:0.646319:0.601134:0.646319:0.000000 +:@0.615756:0.651582:0.630745:0.651582:0.630745:0.634188:0.615756:0.634188:0.000000 1=2,:@0.631669:0.651611:0.665518:0.651611:0.665518:0.635113:0.631669:0.635113:0.000000:0.000000:0.000000:0.000000 f:@0.676114:0.651726:0.680410:0.651726:0.680410:0.635258:0.676114:0.635258:0.000000 1 =1 1 1=3.:@0.689735:0.651611:0.805772:0.651611:0.805772:0.635113:0.689735:0.635113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ():@0.683023:0.653024:0.703926:0.653024:0.703926:0.632325:0.683023:0.632325:0.000000:0.000000 + +:@0.726149:0.651582:0.770998:0.651582:0.770998:0.634188:0.726149:0.634188:0.000000:0.000000:0.000000 :@0.744245:0.574979:0.748387:0.574979:0.748387:0.558511:0.744245:0.558511:0.000000 valores :@0.427967:0.592215:0.485416:0.592215:0.485416:0.575717:0.427967:0.575717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f(x) x:@0.485416:0.592330:0.515760:0.593072:0.515760:0.576603:0.485416:0.575861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para | | 1,:@0.516337:0.592215:0.613252:0.592956:0.613252:0.576459:0.516337:0.575717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x x:@0.555850:0.592330:0.578305:0.593072:0.578305:0.576603:0.555850:0.575861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.567467:0.591998:0.583514:0.591998:0.583514:0.577351:0.567467:0.577351:0.000000 [–1,1]::@0.587753:0.592215:0.632853:0.592215:0.632853:0.575717:0.587753:0.575717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.493882:0.593072:0.498178:0.593072:0.498178:0.576603:0.493882:0.576603:0.000000 :@0.498178:0.593072:0.502320:0.593072:0.502320:0.576603:0.498178:0.576603:0.000000 ( ):@0.500792:0.594369:0.523254:0.594369:0.523254:0.573670:0.500792:0.573670:0.000000:0.000000:0.000000 =:@0.524863:0.592956:0.535671:0.592956:0.535671:0.576459:0.524863:0.576459:0.000000 :@0.535671:0.592956:0.539813:0.592956:0.539813:0.576459:0.535671:0.576459:0.000000 x:@0.539158:0.593072:0.546633:0.593072:0.546633:0.576603:0.539158:0.576603:0.000000 +:@0.546633:0.592927:0.561622:0.592927:0.561622:0.575533:0.546633:0.575533:0.000000 :@0.567979:0.592956:0.572121:0.592956:0.572121:0.576459:0.567979:0.576459:0.000000 :@0.578305:0.593072:0.582447:0.593072:0.582447:0.576603:0.578305:0.576603:0.000000 +:@0.587013:0.592927:0.602002:0.592927:0.602002:0.575533:0.587013:0.575533:0.000000 :@0.613252:0.592956:0.617395:0.592956:0.617395:0.576459:0.613252:0.576459:0.000000 g x:@0.626141:0.593072:0.648546:0.593072:0.648546:0.576603:0.626141:0.576603:0.000000:0.000000:0.000000 ( ):@0.633578:0.594369:0.656041:0.594369:0.656041:0.573670:0.633578:0.573670:0.000000:0.000000:0.000000 =:@0.657650:0.592956:0.668457:0.592956:0.668457:0.576459:0.657650:0.576459:0.000000 :@0.668457:0.592956:0.689283:0.592956:0.689283:0.576459:0.668457:0.576459:0.000000:0.000000:0.000000 x:@0.689283:0.593072:0.696758:0.593072:0.696758:0.576603:0.689283:0.576603:0.000000 :@0.696758:0.593072:0.700900:0.593072:0.700900:0.576603:0.696758:0.576603:0.000000 1:@0.713885:0.592956:0.722381:0.592956:0.722381:0.576459:0.713885:0.576459:0.000000 , :@0.722381:0.592956:0.729278:0.592956:0.729278:0.576459:0.722381:0.576459:0.000000:0.000000 x:@0.735905:0.593072:0.743380:0.593072:0.743380:0.576603:0.735905:0.576603:0.000000 :@0.743380:0.593072:0.747522:0.593072:0.747522:0.576603:0.743380:0.576603:0.000000 [ :@0.759302:0.594369:0.769473:0.594369:0.769473:0.573670:0.759302:0.573670:0.000000:0.000000 1,1 .:@0.779614:0.592956:0.807471:0.592956:0.807471:0.576459:0.779614:0.576459:0.000000:0.000000:0.000000:0.000000:0.000000 ]:@0.799360:0.594369:0.804716:0.594369:0.804716:0.573670:0.799360:0.573670:0.000000 f:@0.460635:0.625762:0.464931:0.625762:0.464931:0.609293:0.460635:0.609293:0.000000 1 = 1:@0.489065:0.625645:0.540541:0.625645:0.540541:0.609147:0.489065:0.609147:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.467549:0.627058:0.446819:0.627058:0.446819:0.606359:0.467549:0.606359:0.000000 ):@0.495772:0.627058:0.475043:0.627058:0.475043:0.606359:0.495772:0.606359:0.000000 +:@0.540310:0.625616:0.555298:0.625616:0.555298:0.608222:0.540310:0.608222:0.000000 1 1=1,:@0.573874:0.625645:0.633945:0.625645:0.633945:0.609147:0.573874:0.609147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 +:@0.584973:0.625616:0.599961:0.625616:0.599961:0.608222:0.584973:0.608222:0.000000 f:@0.648837:0.625761:0.653133:0.625761:0.653133:0.609292:0.648837:0.609292:0.000000 1:@0.679572:0.616648:0.688068:0.616648:0.688068:0.600150:0.679572:0.600150:0.000000 2:@0.678936:0.636847:0.687432:0.636847:0.687432:0.620349:0.678936:0.620349:0.000000 =:@0.698261:0.625645:0.709069:0.625645:0.709069:0.609147:0.698261:0.609147:0.000000 1:@0.727735:0.616648:0.736231:0.616648:0.736231:0.600150:0.727735:0.600150:0.000000 2:@0.727099:0.636847:0.735595:0.636847:0.735595:0.620349:0.727099:0.620349:0.000000 +:@0.738885:0.625616:0.753874:0.625616:0.753874:0.608222:0.738885:0.608222:0.000000 1:@0.774746:0.616648:0.783242:0.616648:0.783242:0.600150:0.774746:0.600150:0.000000 2:@0.774110:0.636847:0.782606:0.636847:0.782606:0.620349:0.774110:0.620349:0.000000 +:@0.788724:0.625616:0.803712:0.625616:0.803712:0.608222:0.788724:0.608222:0.000000 1=1,:@0.804637:0.625645:0.837696:0.625645:0.837696:0.609147:0.804637:0.609147:0.000000:0.000000:0.000000:0.000000 f:@0.428791:0.668631:0.433087:0.668631:0.433087:0.652163:0.428791:0.652163:0.000000 0 =0:@0.443606:0.668516:0.483483:0.668511:0.483483:0.652014:0.443606:0.652018:0.000000:0.000000:0.000000:0.000000 ():@0.435719:0.669924:0.459801:0.669924:0.459801:0.649225:0.435719:0.649225:0.000000:0.000000 + +:@0.485255:0.668482:0.533265:0.668482:0.533265:0.651088:0.485255:0.651088:0.000000:0.000000:0.000000 0:@0.505194:0.668511:0.513690:0.668511:0.513690:0.652014:0.505194:0.652014:0.000000 1=1,:@0.534190:0.668511:0.567249:0.668511:0.567249:0.652014:0.534190:0.652014:0.000000:0.000000:0.000000:0.000000 f:@0.582141:0.668627:0.586437:0.668627:0.586437:0.652158:0.582141:0.652158:0.000000 1:@0.598690:0.659518:0.607186:0.659518:0.607186:0.643020:0.598690:0.643020:0.000000 2:@0.598054:0.679717:0.606550:0.679717:0.606550:0.663219:0.598054:0.663219:0.000000 =:@0.617379:0.668511:0.628186:0.668511:0.628186:0.652014:0.617379:0.652014:0.000000 1:@0.632656:0.659518:0.641152:0.659518:0.641152:0.643020:0.632656:0.643020:0.000000 2:@0.632020:0.679717:0.640516:0.679717:0.640516:0.663219:0.632020:0.663219:0.000000 +:@0.643816:0.668482:0.658804:0.668482:0.658804:0.651088:0.643816:0.651088:0.000000 1:@0.665489:0.659518:0.673985:0.659518:0.673985:0.643020:0.665489:0.643020:0.000000 2:@0.664853:0.679717:0.673349:0.679717:0.673349:0.663219:0.664853:0.663219:0.000000 +:@0.679466:0.668482:0.694455:0.668482:0.694455:0.651088:0.679466:0.651088:0.000000 1=2,:@0.695379:0.668511:0.729228:0.668511:0.729228:0.652014:0.695379:0.652014:0.000000:0.000000:0.000000:0.000000 f:@0.739824:0.668627:0.744121:0.668627:0.744121:0.652158:0.739824:0.652158:0.000000 1 =1 1 1=3.:@0.753445:0.668511:0.869478:0.668511:0.869478:0.652014:0.753445:0.652014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ():@0.746737:0.669924:0.767640:0.669924:0.767640:0.649225:0.746737:0.649225:0.000000:0.000000 + +:@0.789863:0.668482:0.834704:0.668482:0.834704:0.651088:0.789863:0.651088:0.000000:0.000000:0.000000 Sea:@0.427971:0.705320:0.452091:0.705320:0.452091:0.688822:0.427971:0.688822:0.000000:0.000000:0.000000 x :@0.456233:0.705436:0.488040:0.705436:0.488040:0.688967:0.456233:0.688967:0.000000:0.000000:0.000000:0.000000 :@0.467850:0.705103:0.483898:0.705103:0.483898:0.690456:0.467850:0.690456:0.000000 [–1,1]. Si – 1 ≤ x ≤ 0 se tiene::@0.488136:0.705320:0.695255:0.705320:0.695255:0.688822:0.488136:0.688822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.533333:0.705436:0.537475:0.705436:0.537475:0.688967:0.533333:0.688967:0.000000 , :@0.631239:0.705436:0.638232:0.705436:0.638232:0.688967:0.631239:0.688967:0.000000:0.000000 :@0.404236:0.722787:0.408378:0.722787:0.408378:0.706318:0.404236:0.706318:0.000000 f(x) = x + x + = x – x + :@0.427971:0.722787:0.612802:0.722787:0.612802:0.706318:0.427971:0.706318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | | 1:@0.496420:0.722671:0.541193:0.722671:0.541193:0.706173:0.496420:0.706173:0.000000:0.000000:0.000000:0.000000:0.000000 1 = 1 :@0.612802:0.722671:0.664163:0.722671:0.664163:0.706173:0.612802:0.706173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.648886:0.722787:0.655879:0.722787:0.655879:0.706318:0.648886:0.706318:0.000000:0.000000 :@0.404236:0.740022:0.408378:0.740022:0.408378:0.723524:0.404236:0.723524:0.000000 y si 0:@0.427971:0.740022:0.466771:0.740022:0.466771:0.723524:0.427971:0.723524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ≤ x ≤ :@0.466771:0.740137:0.512584:0.740137:0.512584:0.723669:0.466771:0.723669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1, :@0.512584:0.740022:0.532119:0.740022:0.532119:0.723524:0.512584:0.723524:0.000000:0.000000:0.000000:0.000000 f(x) = x + x + = x + x + :@0.532119:0.740137:0.717797:0.740137:0.717797:0.723669:0.532119:0.723669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | | 1:@0.600568:0.740022:0.645341:0.740022:0.645341:0.723524:0.600568:0.723524:0.000000:0.000000:0.000000:0.000000:0.000000 1 = 2 + 1.:@0.717797:0.740022:0.791699:0.740022:0.791699:0.723524:0.717797:0.723524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.753881:0.740137:0.765498:0.740137:0.765498:0.723669:0.753881:0.723669:0.000000:0.000000 :@0.404236:0.757372:0.408378:0.757372:0.408378:0.740875:0.404236:0.740875:0.000000 :@0.404236:0.774723:0.408378:0.774723:0.408378:0.758225:0.404236:0.758225:0.000000 Por otro lado, obtenemos algunos valores de:@0.427971:0.774723:0.743821:0.774723:0.743821:0.758225:0.427971:0.758225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 g(x), x :@0.743821:0.774839:0.824966:0.774839:0.824966:0.758370:0.743821:0.758370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.804776:0.774506:0.820824:0.774506:0.820824:0.759859:0.804776:0.759859:0.000000 [–1,1]::@0.824966:0.774723:0.869681:0.774723:0.869681:0.758225:0.824966:0.758225:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 g:@0.548533:0.792190:0.555969:0.792190:0.555969:0.775721:0.548533:0.775721:0.000000 (–1) = 0, (0) = –1 (1) = –2.:@0.555969:0.792074:0.771239:0.792074:0.771239:0.775576:0.555969:0.775576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 g:@0.617214:0.792190:0.632934:0.792190:0.632934:0.775721:0.617214:0.775721:0.000000:0.000000:0.000000 , g:@0.691423:0.792190:0.709995:0.792190:0.709995:0.775721:0.691423:0.775721:0.000000:0.000000:0.000000:0.000000 :@0.404236:0.809425:0.408378:0.809425:0.408378:0.792927:0.404236:0.792927:0.000000 :@0.404236:0.826775:0.408378:0.826775:0.408378:0.810278:0.404236:0.810278:0.000000 La función :@0.427971:0.826775:0.507459:0.826775:0.507459:0.810278:0.427971:0.810278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f + g :@0.507459:0.826891:0.542503:0.826891:0.542503:0.810422:0.507459:0.810422:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 está definida en [–1,1] como sigue: :@0.542503:0.826775:0.793701:0.826775:0.793701:0.810278:0.542503:0.810278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.427971:0.861477:0.433924:0.861477:0.433924:0.844979:0.427971:0.844979:0.000000 f + g)(x) = f (x) + g(x) = x + x + – x – = x = :@0.433924:0.861593:0.778136:0.861593:0.778136:0.845124:0.433924:0.845124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 | | 1:@0.625305:0.861477:0.670077:0.861477:0.670077:0.844979:0.625305:0.844979:0.000000:0.000000:0.000000:0.000000:0.000000 1 | |:@0.714195:0.861477:0.759160:0.861477:0.759160:0.844979:0.714195:0.844979:0.000000:0.000000:0.000000:0.000000:0.000000 x, si –1 ≤ x < 0,:@0.786189:0.846512:0.889759:0.846512:0.889759:0.830043:0.786189:0.830043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –x, si 0 ≤ x ≤ 1.:@0.786189:0.877685:0.889759:0.877685:0.889759:0.861217:0.786189:0.861217:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404236:0.913529:0.408378:0.913529:0.408378:0.897031:0.404236:0.897031:0.000000 En la Figura 2.1. constan las gráficas de las funciones :@0.427971:0.913529:0.801886:0.913529:0.801886:0.897031:0.427971:0.897031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g f + g.:@0.801886:0.913645:0.878296:0.913645:0.878296:0.897176:0.801886:0.897176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.828318:0.913529:0.844424:0.913529:0.844424:0.897031:0.828318:0.897031:0.000000:0.000000:0.000000 –2:@0.181093:0.765148:0.191931:0.765148:0.191931:0.755461:0.181093:0.755461:0.000000:0.000000 –1:@0.216110:0.765148:0.226949:0.765148:0.226949:0.755461:0.216110:0.755461:0.000000:0.000000 1:@0.289092:0.765148:0.294016:0.765148:0.294016:0.755461:0.289092:0.755461:0.000000 3:@0.245547:0.677543:0.250472:0.677543:0.250472:0.667856:0.245547:0.667856:0.000000 2:@0.245547:0.703824:0.250472:0.703824:0.250472:0.694138:0.245547:0.694138:0.000000 1:@0.245547:0.730106:0.250472:0.730106:0.250472:0.720419:0.245547:0.720419:0.000000 –1:@0.239500:0.782660:0.250339:0.782660:0.250339:0.772974:0.239500:0.772974:0.000000:0.000000 –2:@0.239500:0.808942:0.250339:0.808942:0.250339:0.799255:0.239500:0.799255:0.000000:0.000000 2:@0.324098:0.765156:0.329023:0.765156:0.329023:0.755469:0.324098:0.755469:0.000000 x:@0.356705:0.762367:0.361185:0.762367:0.361185:0.752680:0.356705:0.752680:0.000000 y:@0.244915:0.651584:0.249539:0.651584:0.249539:0.641897:0.244915:0.641897:0.000000 0:@0.247894:0.762367:0.252819:0.762367:0.252819:0.752680:0.247894:0.752680:0.000000 y = f(x):@0.279188:0.709170:0.309270:0.709170:0.309270:0.699483:0.279188:0.699483:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = g(x):@0.282612:0.793729:0.314494:0.793729:0.314494:0.784043:0.282612:0.784043:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y = f + g:@0.283746:0.744295:0.318296:0.744295:0.318296:0.734608:0.283746:0.734608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.310046:0.855794:0.321526:0.855794:0.321526:0.845770:0.310046:0.845770:0.000000 :@0.321526:0.856502:0.324408:0.856502:0.324408:0.845026:0.321526:0.845026:0.000000 Figura 2.1.:@0.324408:0.856502:0.372976:0.856502:0.372976:0.845026:0.324408:0.845026:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Desequilibrio cognitivo:@0.199646:0.199982:0.363493:0.199982:0.363493:0.184510:0.199646:0.184510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Cuál es la definición de :@0.199884:0.228609:0.358352:0.228609:0.358352:0.213546:0.199884:0.213546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 “función nula”?:@0.153341:0.244451:0.250207:0.244451:0.250207:0.229388:0.153341:0.229388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Saberes previos:@0.199646:0.103137:0.307805:0.103137:0.307805:0.087665:0.199646:0.087665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ¿Qué es el dominio de :@0.199884:0.131765:0.348641:0.131765:0.348641:0.116701:0.199884:0.116701:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una función?:@0.153341:0.147607:0.237138:0.147607:0.237138:0.132543:0.153341:0.132543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Recuerda que…:@0.199646:0.317366:0.309406:0.317366:0.309406:0.301894:0.199646:0.301894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f, g:@0.199884:0.346099:0.215398:0.346099:0.215398:0.331062:0.199884:0.331062:0.000000:0.000000:0.000000:0.000000 F(A) :@0.215046:0.345994:0.282975:0.345994:0.282975:0.330930:0.215046:0.330930:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.218476:0.345192:0.230337:0.345192:0.230337:0.334366:0.218476:0.334366:0.000000 ⇒:@0.264615:0.345117:0.279496:0.345117:0.279496:0.331255:0.264615:0.331255:0.000000 f + g F(A), :@0.282623:0.346099:0.365279:0.346099:0.365279:0.331062:0.282623:0.331062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.315938:0.345192:0.327799:0.345192:0.327799:0.334366:0.315938:0.334366:0.000000 que se conoce como propie-:@0.153337:0.361836:0.340073:0.361836:0.340073:0.346772:0.153337:0.346772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dad clausurativa. El grafo o :@0.153337:0.377678:0.329183:0.377678:0.329183:0.362614:0.153337:0.362614:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 gráfico de la función :@0.153337:0.393519:0.293407:0.393519:0.293407:0.378456:0.153337:0.378456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f + g :@0.293407:0.393625:0.329185:0.393625:0.329185:0.378588:0.293407:0.378588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es el :@0.329185:0.393519:0.360548:0.393519:0.360548:0.378456:0.329185:0.378456:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conjunto:@0.153337:0.409361:0.213018:0.409361:0.213018:0.394298:0.153337:0.394298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G(f + g:@0.153337:0.432095:0.196960:0.432095:0.196960:0.417058:0.153337:0.417058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ) = {(:@0.196960:0.431989:0.230610:0.431989:0.230610:0.416926:0.196960:0.416926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x, f(x) + g(x | x:@0.230610:0.432095:0.330346:0.432095:0.330346:0.417058:0.230610:0.417058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 )):@0.300671:0.431989:0.311542:0.431989:0.311542:0.416926:0.300671:0.416926:0.000000:0.000000 :@0.330350:0.431191:0.342211:0.431191:0.342211:0.420365:0.330350:0.420365:0.000000 A:@0.342210:0.431993:0.353046:0.431993:0.353046:0.416930:0.342210:0.416930:0.000000 }.:@0.353134:0.432099:0.360873:0.432099:0.360873:0.417062:0.353134:0.417062:0.000000:0.000000 Glosario:@0.199646:0.499636:0.267111:0.499636:0.267111:0.481954:0.199646:0.481954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función::@0.199884:0.526450:0.253760:0.526450:0.253760:0.511188:0.199884:0.511188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 relación entre :@0.253584:0.526252:0.347128:0.526252:0.347128:0.511188:0.253584:0.511188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos conjuntos que asigna a cada :@0.153341:0.542093:0.361761:0.542093:0.361761:0.527030:0.153341:0.527030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elemento del primero un :@0.153341:0.557935:0.318880:0.557935:0.318880:0.542872:0.153341:0.542872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 elemento del segundo :@0.153341:0.573777:0.302135:0.573777:0.302135:0.558714:0.153341:0.558714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 o ninguno.:@0.153341:0.589619:0.221430:0.589619:0.221430:0.574556:0.153341:0.574556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.146910:0.503368:0.158315:0.501859:0.153112:0.479714:0.141707:0.481223:0.000000 c:@0.150292:0.514337:0.160891:0.512935:0.155808:0.491300:0.145209:0.492703:0.000000 b:@0.160667:0.507120:0.173381:0.505437:0.168249:0.483594:0.155535:0.485277:0.000000