Answer
$f^{-1}(x)=\sqrt[5]{\dfrac{x-3}{2}}$
Work Step by Step
We are given the function:
$$f(x)=2x^5+3.$$
Find the inverse of the function:
$$\begin{align*}
f(x)&=2x^5+3\quad&&\text{Write original function.}\\
y&=2x^5+3\quad&&\text{Replace }f(x)\text{ by }y.\\
x&=2y^5+3\quad&&\text{Switch }x\text{ and }y.\\
x-3&=2y^5\quad&&\text{Subtract }3\text{ from beach side. }\\
\dfrac{x-3}{2}&=y^5\quad&&\text{Divide each side by }2.\\
\sqrt[5]{\dfrac{x-3}{2}}&=y\quad&&\text{Take fifth root of each side.}
\end{align*}$$
The inverse of $f$ is $f^{-1}(x)=\sqrt[5]{\dfrac{x-3}{2}}$.
Graph the function and its inverse:
