Composition: How to prove it is an inverse

If you want to prove that one function is inverse to another, you need to do a composition.

Note: remember f(x) is the original function and f -1 (x) is the inverse function.

1.- You have two options:

Case 1- Instead of writing f-1(x) , substitute x for f(x) in the inverse function

f- -1 (f(x)) =x

Case 2- Instead of writing f(x), substitute x for f- -1(x) in the original function

f (f -1(x)) =x

Example:

Case 1

f(x)=3x-1 and the inverse is f^-1(x)=sqr(x+2)

With the composition it will look something like this:

f (f -1(x)) =3(sqr(x+2)-1

Case 2

It will look like this:

f- -1 (f(x)) =sqr((3x-1)+2)