3.7E: Funciones inversas (Ejercicios)

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30 oct 2022
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- 3.7: Funciones inversas
- 4: Funciones lineales

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Para los siguientes ejercicios, encuentra $f^{-1}(x)$ para cada función.

69. $f(x)=9+10 x$
70. $f(x)=\frac{x}{x+2}$

Para el siguiente ejercicio, busque un dominio en el que la función $f$ sea uno a uno y no decreciente. Escribe el dominio en notación de intervalos. Entonces encuentra el inverso de $f$ restringido a ese dominio.

$f(x)=x^{2}+1$
Dado $f(x)=x^{3}-5$ y $g(x)=\sqrt[3]{x+5}$ :
1. Encontrar $f(g(x))$ y $g(f(x))$ .
2. ¿Qué nos dice la respuesta sobre la relación entre $f(x)$ y $g(x)$ ?

Para los siguientes ejercicios, utilice una utilidad gráfica para determinar si cada función es uno a uno.

73. $f(x)=\frac{1}{x}$
74. $f(x)=-3 x^{2}+x$
75. Si $f(5)=2,$ encuentra $f^{-1}(2)$ .
76. Si $f(1)=4,$ encuentra $f^{-1}(4)$ .

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