Inverse Functions (AQA A Level Maths: Pure): Revision Note

Inverse functions

What is an inverse function?

• An inverse function is the opposite to the original function

• An inverse function is denoted by

• The inverse of a function only exists if the function is one-to-one

• Inverse functions are used to solve equations

  • The solution of  is 

How do I sketch the graph of an inverse function?

• The graphs of a function and its inverse are reflections in the line y = x

What is the domain and range of an inverse function?

• The range of a function will be the domain of its inverse function

• The domain of a function will be the range of its inverse function

How do I find an inverse function using algebra?

• Set y = f(x) and make x the subject

• Then rewrite in function notation

• Domain is needed to fully define a function

• The range of f is the domain of f^-1 (and vice versa)

How are inverse functions related to composite functions?

• A function (f) followed by its inverse (f^-1) will return the input (x)

• ff^-1(x) = f^-1f(x) = x (for all values of x)