Inverse Functions (Cambridge (CIE) AS Maths): Revision Note

Inverse functions

What are inverse functions?

• An inverse function is the opposite to the original function

• It is denoted by f^-1(x)

• An inverse only exists for one-to-one functions

How do I sketch inverse functions?

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

What are the 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 use algebra to find 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)

How are inverse functions and composite functions related?

• 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)