Verify the inverse functions

Question

f(x) = 8x-7 and h(x) = x+7/8

Write simplified expressions for f(h(x)) and h(f(x)) in terms of x

f(h(x)) = Answer

h(f(x)) = Answer

Are functions f and h inverses? Yes or no

Answer 1

Hi Mike I'm Eddie. Are you sure you wrote the h(x) correctly is 8 dividing only the 7?

So is h(x) = x + 7/8 or = x + 7

8

I solve as described. But you simply plug in the other function for x.

f(x) = 8x-7 and h(x) = x+7/8

f(x) = 8( ) - 7

Always use parenthesis this is the first step in the problem. Make sure to give more space then I did also.

f(h(x)) = 8(x + 7/8) - 7

Plug in the h(x) in parenthesis.

f(h(x)) = (8x + 7) - 7

Distribute the 8 inside the parenthesis then subract 7.

f(h(x)) = 8x

Repeat for h(f(x)) ok pretty straightforward if they are inverses the answer would be x. I have a feeling you copied this wrong. If you like further assistance feel free to reach out for a first free session ok.

Answer 2

We note that x+7 must be in the numerator for h(x)

f(h(x)) = f((x+7)/8) = 8(x+7/8 ) - 7 = x + 7 - 7 = x

h(f(x)) = h(8x - 7) = (8x-7+7)/8 = 8x/8 = x