1. Determine if the two functions are inverses. \[ \begin{array}{l} g(x)=\sqrt{9 x-8}+16 \\ \text { and } \\ g^{-1}(x)=\frac{(-16+x)^{2}+8}{9} \text { where } x \geq 16 \end{array} \] Yes, these are inverse functions. No, these are not inverse functions.

Step 1 ：Given the two functions \(g(x)=\sqrt{9x-8}+16\) and \(g^{-1}(x)=\frac{(-16+x)^{2}+8}{9}\) where \(x \geq 16\)

Step 2 ：To determine if these two functions are inverses of each other, we substitute \(g^{-1}(x)\) into \(g(x)\) and see if we get \(x\)

Step 3 ：Substituting \(g^{-1}(x)\) into \(g(x)\), we get \(\sqrt{(x - 16)^{2}} + 16\)

Step 4 ：The result of this substitution is \(x\), which is the identity function

Step 5 ：Since the result is the identity function, the two functions are inverses of each other

Step 6 ：\(\boxed{\text{Yes, these are inverse functions}}\)