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.

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Presentation transcript:

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