Use the functions given by $f ( x ) = \frac { 1 } { 64 } x - 4$ and g(x)= x³ to find g^-1 _º f^-1. ? A) $4 \sqrt [ 3 ] { ( 4 - x ) }$ B) $- 4 \sqrt [ 3 ] { ( x + 4 ) }$ C) $- 4 \sqrt [ 3 ] { ( x - 4 ) }$ D) $4 \sqrt [ 3 ] { ( x - 4 ) }$ E) $4 \sqrt [ 3 ] { ( x + 4 ) }$

Question

Quizplus · Accepted Answer

Given $f(x) = \frac{1}{64}x - 4$ and $g(x) = x^{13}$, to find $g^{-1}(f^{-1}(x))$, we first find the inverse functions of $f$ and $g$. The inverse of $f(x)$, $f^{-1}(x)$, is found by solving $y = \frac{1}{64}x - 4$ for $x$, which gives $x = 64(y + 4)$. The inverse of $g(x) = x^{13}$, $g^{-1}(x)$, is $x^{1/13}$. Substituting $f^{-1}(x)$ into $g^{-1}(x)$ gives $g^{-1}(f^{-1}(x)) = (64(x + 4))^{1/13} = 4\sqrt[3]{x + 4}$, which matches choice E.

Use the Functions Given By f(x)=164x−4f ( x ) = \frac { 1 } { 64 } x - 4f(x)=641​x−4

Use the Functions Given By $f ( x ) = \frac { 1 } { 64 } x - 4$