To find the domain of the inverse function \( h^{-1}(x) \), we need to determine the range of the original function \( h(x) \).
Given \( h(x) = {(-1, 4), (0, 5), (1, -6), (3, 8)} \), we can see that the pairs are in the form \( (x, h(x)) \).
The values of \( h(x) \) are:
- \( h(-1) = 4 \)
- \( h(0) = 5 \)
- \( h(1) = -6 \)
- \( h(3) = 8 \)
The range of \( h(x) \) consists of the \( y \)-values (outputs) which are: \( 4, 5, -6, 8 \).
Thus, the domain of \( h^{-1}(x) \) is exactly the same as the range of \( h(x) \).
So the domain of \( h^{-1}(x) \) is \( { -6, 4, 5, 8 } \).
The correct response is: \[ { -6, 4, 5, 8 } \]