Step 1 :Consider the function $g$, which is a one-to-one function with values $g(9)=-4$ and $g(-2)=-1$.
Step 2 :The inverse function $g^{-1}$ will reverse these mappings, so $g^{-1}(-4) = 9$ and $g^{-1}(-1) = -2$.
Step 3 :Therefore, the correct answers are $g^{-1}(-4) = 9$ and $g^{-1}(-1) = -2$.
Step 4 :Final Answer: \(\boxed{g^{-1}(-4) = 9, g^{-1}(-1) = -2}\)