Find the inverse function of $f$.
$f ( x ) = x ^ { 5 } - 1$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } - 1$
B) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 1$
C) $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x - 1 }$
D) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x + 1 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 1$

Question

Quizplus · Accepted Answer

To find the inverse function, swap $x$ and $y$ and solve for $y$. Starting with $y = x^5 - 1$, we swap to get $x = y^5 - 1$, and then solve for $y$ to get $y = \sqrt[5]{x + 1}$, which matches option D.

Find the Inverse Function Of fff f(x)=x5−1f ( x ) = x ^ { 5 } - 1f(x)=x5−1

Find the Inverse Function Of $f$ $f ( x ) = x ^ { 5 } - 1$