Introduction to Inverse Functions

When you get to pre-calculus, you might have to learn inverse functions....What is that? It's basically, a function that undoes another function.Yea, what does that mean? Well, let me show you how it is done and maybe then you will have a better understanding.

lets take the f(x)=x+1. We want to find the inverse.

YOU SHOULD BE COMFORTABLE WITH REARRANGING EQUATIONS

Follow these steps:

1. set f(x)=y

2.y=x+1

3.swap the x's with the y's.so, in this case, it'll look something like this

      x=y+1

4. Rearrange to make y the subject.

  Lets do it: y=x-1

now...functions are denoted as f(x)...inverse functions are denoted as f^-1(x)

so your final answer will be f^-1(x)=x-1

The highlighted part is the most important, so be sure to memorize it!

Lets do another problem with the Step by Step approach:

Find the inverse of f(x)=3x+2

1. f(x)=y

2. y=3x+2

3. x=3y+2 (I swapped the x's' with the y's, its that simple)

4. Rearrange---

x=3y+2

x-2=3y+2-2

x-2=3y

(x-2)/3=3y/3

y=(x-2)/3

so your answer is f^-1(x) =(x-2)/3

A simple introduction...Later, we're going to learn how to map out inverse functions, graph them, and more.