A continuación se demuestra, aplicando diferentes propiedades aritméticas (y algunos truquitos) que si [math]9=4+5[/math], entonces [math]3=2[/math].[br][br]Lógicamente, hay un error en alguno de los pasos, ¿podrás averiguarlo?
¿En qué paso se comete el error?[br]¿Qué propiedad están aplicando de manera incorrecta?
[color=#ff0000]El error se comete en el penúltimo paso, cuando quitan las raíces.[br]La propiedad que se aplica es:[br] [/color][math]\sqrt{x^2}=x[/math][color=#ff0000][br]Esto solo es cierto si [/color][math]x\ge0[/math][color=#ff0000].[br][br]En ese paso hacen [/color][math]\sqrt{\left(2-\frac{5}{2}\right)^2}=2-\frac{5}{2}[/math][color=#ff0000], pero esto es imposible ya que [/color][math]2-\frac{5}{2}=-\frac{1}{2}<0[/math]
Veamos desde el punto de vista de la composición de funciones y las funciones inversas, porqué sucede esto.[br][br]Consideremos la función [math]f\left(x\right)=x^2[/math]. como todos sabemos, la operación contraria a elevar al cuadrado es la raíz cuadrada. Entonces podríamos suponer que la función inversa de [math]f\left(x\right)[/math] es [math]f^{-1}\left(x\right)=\sqrt{x}[/math].[br][br]Según la definición de la función inversa se tiene que cumplir que [math]f\circ f^{-1}\left(x\right)=f^{-1}\circ f\left(x\right)=id\left(x\right)=x[/math].[br][br]Observa las graficas de las dos funciones, así como de las composiciones entre ellas manipulando el siguiente Applet:
¿Cómo es la gráfica de [math]f\left(x\right)[/math]?[br]¿Cuál es su dominio?
[color=#ff0000]Es una parábola con el vértice en [/color][math]\left(0,0\right)[/math][color=#ff0000] y [/color][math]Dom\left(f\right)=\mathbb{R}[/math]
¿Cómo es la gráfica de [math]f^{-1}\left(x\right)[/math]?[br]¿Cuán es su dominio?
[color=#ff0000]Es media parábola tumbada, ya que si tumbamos la parábola entera, la curva que se obtiene no puede ser la gráfica de una función, pues muchos valores de su dominio tendrían 2 imágenes.[br][/color][math]Dom\left(f^{-1}\right)=\text{[0,+\infty[}[/math]
¿Se cumple esta vez que [math]f\circ f^{-1}\left(x\right)=f^{-1}\circ f\left(x\right)[/math] ?
[color=#ff0000]Observando las gráficas podemos decir que ambas composiciones solo coinciden entre ellas y con la identidad en [/color][math]\text{[0,+\infty[}[/math][color=#ff0000].[br][br]Si expresamos analíticamente ambas funciones tendremos:[br][br][img]data:image/png;base64,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[/img][br]pero por otro lado:[br][img]data:image/png;base64,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[/img][br][br][/color]
Como conclusión, diremos que la función [math]f\left(x\right)=x^2[/math] no tiene inversa, en general.[br][br]Igualmente, en general no podemos afirmar que [br][img]data:image/png;base64,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[/img][br]ya que esto solo es cierto si [math]x\ge0[/math].[br][br]La simplificación de raíces con cuadrados podríamos expresarla con dos propiedades:[br][br][img]data:image/png;base64,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[/img][br][img]data:image/png;base64,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[/img]