Question

Find the inverse of f(x) = 4x + 12

Answer 1

f(x) = 4x + 12

y = 4x + 12 ... replace f(x) with y

x = 4y + 12 ... swap x and y

Answer 2

now solve for y to get your inverse function

Answer 3

y = 4x + 12

Swapping x and y.

x = 4y + 12

Now solve for y = again.
4y = x-12
4y/4 = (x-12)/4
y = x/4 - 3

Voila. There's your inverse equation. (I hope I got it right anyway.)