Question

What is the inverse of the function h(x) = 5 over 2 x + 4

Answer 1

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