Answer
$f^{-1}(x)=\sqrt[6]x,x\geq 0$
Work Step by Step
We are given the function:
$$f(x)=x^6,x\geq 0.$$
Find the inverse of the function:
$$\begin{align*}
f(x)&=x^6\quad&&\text{Write original function.}\\
y&=x^6\quad&&\text{Replace }f(x)\text{ by }y.\\
x&=y^6\quad&&\text{Switch }x\text{ and }y.\\
\sqrt[6]x&=y\quad&&\text{Take sixth root of each side.}
\end{align*}$$
The inverse of $f$ is $f^{-1}(x)=\sqrt[6]x, x\geq 0$.
Graph the function and its inverse:
