$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$
A)$f ^ { - 1 } ( x ) = \frac { 17 } { 7 } ^ { \frac { 7 } { 17 } }$
B)$f ^ { - 1 } ( x ) = x ^ { - \frac { 7 } { 17 } }$
C) $f ^ { - 1 } ( x ) = x ^ { 119 }$
D)$f ^ { - 1 } ( x ) = x ^ { - \frac { 17 } { 7 } }$
E)$f^{-1}(x)=x^{\frac{17}{7}}$

Question

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$ 
A)$f ^ { - 1 } ( x ) = \frac { 17 } { 7 } ^ { \frac { 7 } { 17 } }$
B)$f ^ { - 1 } ( x ) = x ^ { - \frac { 7 } { 17 } }$
C) $f ^ { - 1 } ( x ) = x ^ { 119 }$
D)$f ^ { - 1 } ( x ) = x ^ { - \frac { 17 } { 7 } }$
E)$f^{-1}(x)=x^{\frac{17}{7}}$

Quizplus · Accepted Answer

We want to find $f^{-1}(x)$, which is the inverse of $f(x)$. To do this, we switch the $x$ and $y$ variables and solve for $y$:
$$y = x^\frac{7}{17}$$
$$x = y^\frac{7}{17}$$
$$y^\frac{17}{7} = x$$
$$y = x^\frac{17}{7}$$
Therefore, $f^{-1}(x) = x^\frac{17}{7}$. The answer is $\boxed{	ext{(D)}}$.

Find f−1(x) if f(x)=x717\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } } Find f−1(x) if f(x)=x177​

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { \frac { 7 } { 17 } }$