Inverse Functions (DP IB Applications & Interpretation (AI)): Revision Note

Inverse Functions

What is an inverse function?

• Only one-to-one functions have inverses

• A function has an inverse if its graph passes the horizontal line test

  • Any horizontal line will intersect with the graph at most once

• Given a function we denote the inverse function as 

• An inverse function reverses the effect of a function

  • means 

• Inverse functions are used to solve equations

  • The solution of is 

What are the connections between a function and its inverse function?

• The domain of a function becomes the range of its inverse

• The range of a function becomes the domain of its inverse

• The graph of  is a reflection of the graph in the line 

  • Therefore solutions to  or  will also be solutions to 

    • There could be other solutions to  that don't lie on the line