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)
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