Question

`f(x)=(x+9)/(4) \\g(x)=4x-9`

Show your work to prove that the inverse of f(x) is g(x)

Answer 1

Below.

Explanation:

If f(x) is the inverse then f(g(x)) = x.

f(g(x)) = ((4x - 9) + 9) / 4

= 4x/4

= x.

So it is true.

It can also be shown that g(f(x)) = x.

Answer 2

inverse of f(x) is g(x)

Explanation:

f(x) = (x+9)/4

g(x) = 4x-9

f^-1(x) = g(x)

Let y = (x+9)/4

4y = x + 9 (make x the subject)

x = 4y - 9

f^-1(x) = 4x - 9

= g(x) (shown)