Question

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

Answer 1

Given the function f(x)f(x) we want to find the inverse function, f−1(x)f−1(x).

First, replace f(x)f(x) with yy. This is done to make the rest of the process easier.

Replace every xx with a yy and replace every yy with an xx.

Solve the equation from Step 2 for yy. This is the step where mistakes are most often made so be careful with this step.

Replace yy with f−1(x)f−1(x). In other words, we’ve managed to find the inverse at this point!

Verify your work by checking that(f∘f−1)(x)=x(f∘f−1)(x)=xand(f−1∘f)(x)=x(f−1∘f)(x)=xare both true. This work can sometimes be messy making it easy to make mistakes so again be careful.