Chapter 1.5 - Inverse Functions

The inverse of a function is when all of the x and y coordinates are switched.

Example: The inverse of (1,2) (2,4) (3,6) is (2,1) (4,2) (6,3)

To find the inverse of a function you must switch the x and y variable and then solve for y. This is denoted by . The domain of must be equal to the range of , and the range of must be equal to the domain of .

Example: If then

To verify that you found the inverse of the function you can compose one to the other and it should equal x. If it doesn't then you did something wrong.

Example:

The graph of a function and its inverse are reflected across the line .

Example: The red graph is and the green graph is .

Not all functions have inverses that are functions.

Example:

The red graph is

The green graph is the inverse which is

The inverse if the red graph (green graph) is not a function because it doesn't pass the vertical line test.