5.3 INVERSE FUNCTIONS OBJECTIVES VERIFY ONE FUNCTION IS THE INVERSE OF ANOTHER DETERMINE WHETHER A FUNCTION HAS AN INVERSE FIND THE DERIVATIVE OF AN INVERSE FUNCTION AP Calculus AB
Inverse Functions
Write the Two Functions In order to find the inverse, we must switch the order of the operations
Verify Functions are Inverses
Graphs of Inverse Functions Inverses are reflections across y = x.
Criteria for an Inverse For a function to have an inverse, the function must be monotonic. Increasing or decreasing on the entire domain Passes a horizontal line test
Find the Inverse In order to find an inverse, simply switch the x and y variables and solve for y. The y-variable now represents the inverse function
Example
Derivatives of Inverse Functions
Formative Assessment