The domain of a one-to-one function $g$ is $(-\infty, 0]$, and its range is $[8, \infty)$. State the domain and the range of $g^{-1}$ The domain of $\mathrm{g}^{-1}$ is (Type your answer in interval notation.)

Step 1 ：The domain of the inverse function $g^{-1}$ is the range of the original function $g$. Similarly, the range of the inverse function $g^{-1}$ is the domain of the original function $g$. Therefore, the domain of $g^{-1}$ is $[8, \infty)$ and the range of $g^{-1}$ is $(-\infty, 0]$.

Step 2 ：Final Answer: \(\boxed{\text{The domain of } g^{-1} \text{ is } [8, \infty) \text{ and the range of } g^{-1} \text{ is } (-\infty, 0]}\)