The given function is
h(x) = 5x/2 + 4
The first step is to replace h(x) with y. We have
y = 5x/2 + 4
The next step is to interchange x and y and solve for y. We have
x = 5y/2 + 4
Subtracting 4 from both sides of the equation, we have
x - 4 = 5y/2 + 4 - 4
x - 4 = 5y/2
Multiplying both sides of the equation by 2, we have
2(x - 4) = 5y/2 * 2
2(x - 4) = 5y
Dividing both sides of the equation by 5, we have
2(x - 4)/5 = 5y/5
y = 2(x - 4)/5
The next step is to replace y with h^-1(x). Thus,
h^-1(x) = 2(x - 4)/5
