The one-to-one functions $g$ and $h$ are defined as follows.
$$\begin{array}{l}g=\{(-5,5),(0,-7),(5,4),(7,0)\}\\ h(x)=3x+14\end{array}$$
Find the following.
$g^{-1}(5)=◻$
$h^{-1}(x)=◻$
$(h^{-1}\circ h)(-5)=◻$

Step 1 ：The first question asks for the inverse of function g at 5. This means we need to find the x-value that corresponds to the y-value of 5 in the function g. Looking at the function g, we can see that the pair (-5,5) is present. This means that $g^{-1}(5)$ is -5.

Step 2 ：The second question asks for the inverse of function h. The function h is given as $h(x)=3x+14$. To find the inverse of this function, we need to swap x and y and solve for y. This will give us the inverse function $h^{-1}(x)$.

Step 3 ：The third question asks for the value of $(h^{-1}\circ h)(-5)$. This is the composition of the inverse of h and h at -5. Since the inverse of a function undoes the operation of the function, the composition of a function and its inverse will just give the original input. Therefore, $(h^{-1}\circ h)(-5)$ should be -5.

Step 4 ：Final Answer: $g^{-1}(5)=\boxed{{\displaystyle -5}}$, $h^{-1}(x)=\boxed{{\displaystyle \frac{x-14}{3}}}$, $(h^{-1}\circ h)(-5)=\boxed{{\displaystyle -5}}$