Inverse Functions

This lesson covers: 

  1. What inverse functions are
  2. How to find an inverse function

What are inverse functions?


An inverse function f-1(x) is a function which reverses the operations of the original function f(x).

Diagram showing the process of an inverse function f-1 undoing the operations of the original function f

f-1(x) is the inverse function of f(x).

f-1(x) undoes the operations performed by f(x).

Finding the inverse function


The process of determining the inverse involves a few clear steps:

  1. Write out the equation of the function using y instead of x.
  2. Set this expression equal to x.
  3. Rearrange to make y the subject.
  4. Replace y with f-1(x).

Worked example 1: Inverse functions


Given that f(x) = 12x + 3, find f-1(x).

Worked example 2:  Inverse functions


Given that f(x) = 2x - 3, find f-1(x).

Worked example 3:  Inverse functions


Given that f(x) = -5x + 7, find f-1(x).

Find the inverse of the function f(x) = 3x +4.

f−1(x)=3x+4​
f−1(x)=x−43​
f−1(x)=3x−4​
f−1(x)=34−x​

0

/

1

Find the inverse of the function f(x) = 3x - 2.

f−1(x)=−34−x​
f−1(x)=3x+2​
f−1(x)=x−23​
f−1(x)=2x+3​

0

/

1

Find the inverse of the function f(x) = 4x - 1.

f−1(x)=−14−x​
f−1(x)=4x+1​
f−1(x)=x−14​
f−1(x)=3x+4​

0

/

1

Find the inverse of the function f(x) = 2x2 - 3.

f−1(x)=√x−32​​
f−1(x)=√x+32​​
f−1(x)=√2x−3​​
f−1(x)=√2x+3​​

0

/

1

Find the inverse of the function f(x) = 3x2 + 4.

f−1(x)=√x−43​​
f−1(x)=√3x−4​​
f−1(x)=√3x+4​​
f−1(x)=√24x−3​​

0

/

1