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?
- Replace f(x) with y
- Interchange x and y
- Solve the equation for y
- 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)
Finding the Inverse of a Function
This video outlines the procedure and do two complete examples of finding the inverse of a function.
Examples:
- If f(x) = √(x + 4) - 3, find f-1(x)
- If f(x) = (5x - 3)/(2x + 1), find f-1(x)
Inverse Functions Part 1
This video demonstrates how to find an inverse of a function.
Example:
Find the inverse of f(x) = 3x - 2
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)
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.