Question

Find the inverse of the function$f\left(x\right)=x^5-9$.

Short answer

The inverse of the function is $f^{-1}\left(x\right)=\sqrt[5]{x+9}$.

Step-by-step solution

Step 1. Given information.

Consider the given function,

$f\left(x\right)=x^5-9$

Replace $f\left(x\right)$with $y$,

$y=x^5-9$

Replace $x$with $y$and vice-versa,

$x=y^5-9$

Step 2. Solve for y.

Add $9$on both sides,

role="math" localid="1645025732251" $$\begin{gathered} x+9=y^5 \\ y=\sqrt[5]{x+9} \end{gathered}$$

Replace $y$with role="math" localid="1645025745429" $f^{-1}\left(x\right)$,

$f^{-1}\left(x\right)=\sqrt[5]{x+9}$