The one-to-one functions g and h are defined as follows.?

The easiest function here is g^-1(x) because you are given all the ordered pairs of g(x) .

g^-1(x) reverses the ordered pairs so they are (y,x).

For g^-1(-5), look for the ordered pair in g(x) that has (x, -5). That would be (5, -5).

Then g^-1(-5) = 5

To determine h^-1(x), rewrite the function rule of h(x) = y = 3x - 4

For h^-1(x), then x = 3y - 4

x = 3y - 4

3y = x + 4

y = (x + 4)/3

h^-1(x) = (x + 4)/3

I regret that I do not know what you mean by (h * h^(-1)) (5)

Should it be h(h^-1(5))?

h(h^-1(5)) = 5, because a function of its inverse is the identity function, that is, the value of x is unchanged.