The one-to-one functions $g$ and $h$ are defined as follows. \[ \begin{array}{l} g=\{(-8,-7),(-1,-8),(2,0),(9,2)\} \\ h(x)=3 x-8 \end{array} \] Find the following. \[ \begin{array}{c} g^{-1}(-8)= \\ h^{-1}(x)= \\ \left(h \circ h^{-1}\right)(1)= \end{array} \]

Step 1 ：Define the function g as g = {-8: -7, -1: -8, 2: 0, 9: 2}.

Step 2 ：Find the inverse of the function g at -8. This is the x value in the pair (x, y) in the definition of g where y = -8. So, \(g^{-1}(-8)\) is -1.

Step 3 ：Define the function h as \(h(x) = 3x - 8\).

Step 4 ：Find the inverse function of h. Swap x and y and solve for y to get \(h^{-1}(x) = \frac{x + 8}{3}\).

Step 5 ：Find the composition of the function h with its inverse at 1. Since the inverse of a function 'undoes' the operation of the function, the composition of a function with its inverse should be the identity function, which returns its input unchanged. Therefore, \(\left(h \circ h^{-1}\right)(1)\) is 1.

Step 6 ：Final Answer: \(g^{-1}(-8) = \boxed{-1}\), \(h^{-1}(x) = \boxed{\frac{x + 8}{3}}\), \(\left(h \circ h^{-1}\right)(1) = \boxed{1}\)