Answer
domain: $[0,\infty)$
range: $(-\infty,0]$
Work Step by Step
The domain of $g$ is the range of $g^{-1}$ and the range of $g$ is the domain of $g^{-1}$.
Hence, the inverse function $g^{-1}$ has:
domain: $[0,\infty)$
range: $(-\infty,0]$