Inverse Functions

Examples, videos and solutions to help GCSE Maths students learn how to find the inverse of a function.

What is a one-to-one function?
In a one-to-one function every element in the domain is paired with a unique element in the range
and every element in the range is paired with a unique element in the domain.

Only one-to-one functions can have inverse functions.

How to find the inverse of a function?

1. Replace f(x) with y
   
2. Interchange x and y
   
3. Solve the equation for y
   
4. Replace y with f^-1(x)

The following diagram shows how to find the inverse of a function. Scroll down the page for more examples and solutions.

 

Inverse functions: Introduction
This video introduces inverse functions, what they are, notation and how to find them.
Example:
If f(x) = (3x - 2)/8, find f^-1(x)

• Show Video

Finding the Inverse of a Function
This video outlines the procedure and do two complete examples of finding the inverse of a function.
Examples:

1. If f(x) = √(x + 4) - 3, find f^-1(x)
   
2. If f(x) = (5x - 3)/(2x + 1), find f^-1(x)
   

• Show Step-by-step Solutions

Inverse Functions Part 1
This video demonstrates how to find an inverse of a function.
Example:
Find the inverse of f(x) = 3x - 2

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Inverse Functions Part 2
This video demonstrates a second example for how to find an inverse function.
Example:
Find the inverse of f(x) = 3x/(x - 1)

• Show Step-by-step Solutions

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