The given functions are
g=((-7, 5), (0, 7), (8, -2), (9, 0))
and
h(x) = 2x - 13
To find g^-(0), we would find the value of x when y is 0
Looking at the function, where y = 0, x = 9
Thus,
g^-(0) = 9
The second function is
h(x) = 2x - 13
We would replace h(x) with y. We have
y = 2x - 13
The next step is to interchange x and y and solve for y. We have
x = 2y - 13
x + 13 = 2y
y = (x + 13)/2
We would replace y with h^-1(x). We have
h^-1(x) = (x + 13)/2
To find (h^-1 o h)(4), the first step is to find (h^-1 o h)(x). To do this, we would substitute x = 2x - 13 into h^-1(x) = (x + 13)/2. We have
(h^-1 o h)(x) = (2x - 13 + 13)/2
(h^-1 o h)(x) = 2x/2 = x
To find (h^-1 o h)(4), we would substitute x = 4 into (h^-1 o h)(x) = x. We have
(h^-1 o h)(4) = 4