Answer
$g^{-1}(x)=\sqrt[5]{\dfrac{7-x}{7}}$
Work Step by Step
We are given the function:
$$g(x)=-7x^5+7.$$
Find the inverse of the function:
$$\begin{align*}
g(x)&=-7x^5+7\quad&&\text{Write original function.}\\
y&=-7x^5+7\quad&&\text{Replace }g(x)\text{ by }y.\\
x&=-7y^5+7\quad&&\text{Switch }x\text{ and }y.\\
x-7&=-7y^5\quad&&\text{Subtract }7\text{ from beach side. }\\
\dfrac{7-x}{7}&=y^5\quad&&\text{Divide each side by }-7.\\
\sqrt[5]{\dfrac{7-x}{7}}&=y\quad&&\text{Take fifth root of each side.}
\end{align*}$$
The inverse of $g$ is $g^{-1}(x)=\sqrt[5]{\dfrac{7-x}{7}}$.
Graph the function and its inverse:
