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

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)