Question

In the following exercises, find the inverse of each function.

$f\left(x\right)=\sqrt[5]{x-1}$

Short answer

The inverse is$f^{-1}\left(x\right)=x^5+1$

Step-by-step solution

Step 1. Given

A function is given as$f\left(x\right)=\sqrt[5]{x-1}$

Step 2. Calculation

Let $f\left(x\right)=y$,

$y=f\left(x\right)=\sqrt[5]{x-1}$

Simplify and find the value of $x$in terms of $y$and that will be the inverse of function.

$$\begin{gathered} y=\sqrt[5]{x-1} \\ {y}^5=x-1 \\ x=y^5+1 \end{gathered}$$

Therefore, the inverse is$f^{-1}\left(x\right)=x^5+1$