Inverse Functions (AQA A Level Maths: Pure)

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 

  

Graphs of inverse functions

 

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

Domain and range of inverse functions

• 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 work out an inverse function?

• 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)

... and finally …

• 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)