Help Please Intermediate Algebra

Wait, but @ikleyn, check out my answer here:

Let $y=f(x)$, so $y$ can take on any value from $-3$ to $5$, inclusive. Then, $y^2$ can take on any value from 0 to 25, inclusive. )If we take any value from $-3$ to $0$ and square it, we get a value from 0 to 9. And if we take any value from 0 to 5 and square it, we get a value from 0 to 25.) Therefore, the range of $g(x)$ is $\boxed{[0,25]}$