The inverse of the function h(x) = -5x - 7 can be found by following these steps:
Swap x and y: Replace x with y and y with x. This will give you: y = -5x - 7.
Solve for x: Isolate x by adding 7 to both sides and then dividing both sides by -5. This will give you: x = (y + 7) / -5.
Rewrite the equation: Replace y with h^-1(x) to represent the inverse function. This gives you: h^-1(x) = (x + 7) / -5.
Therefore, the inverse of h(x) = -5x - 7 is h^-1(x) = (x + 7) / -5.