Answer
Inverse: $y=\sqrt[3]{\dfrac{x-10}{2}}$
The inverse is a function.
Work Step by Step
To find the inverse of the given function, perform the followiong steps:
(1) Interchange $ x$ and $y$.
$$x=2y^3+10$$
(2) Solve for $y$.
\begin{align*}
x-10&=2y^3 &\text{Subtract 10 from each side.}\\\\
\frac{x-10}{2}&=\frac{2y^3}{2} &\text{Divide 2 to both sides.}\\\\
\frac{x-10}{2}&=y^3\\\\
\sqrt[3]{\frac{x-10}{2}}&=\sqrt[3]{y^3} &\text{Take the cube root of both sides.}\\\\
\sqrt[3]{\frac{x-10}{2}}&=y\\\\
\end{align*}
Note that for $y=\sqrt[3]{\dfrac{x-10}{2}}$, for every value of $x$, there is only one corresponding value for $y$.
Thus, the inverse of the given function is also a function.
