Inverse of a Function Section 5.6 Beginning on Page 276

What is the Inverse of a Function? The inverse of a function is a generic equation to find the input of the original function when given the output [finding x when given y]. Inverse functions undo each other. To find the inverse of a function we switch x and y and solve for y. We can then write a rule for the inverse function. If we are given (or find) a set of coordinate pairs for a function, we can swap the values of x and the values of y and we will have a set of coordinate pairs for the inverse of the function. You can verify if one function is the inverse of the other by composing the functions. The inverse of a function might not also be a function. If the graph of a function passes the horizontal line test, its inverse is also a function.

Writing a Formula for the Input of a Function The input is -5 when the output is -7

Inverse Functions

Finding the Inverse of a Linear Function Or

Inverses of Nonlinear Functions

Finding the Inverse of a Quadratic Function

The Horizontal Line Test

Finding the Inverse of a Cubic Function First, sketch the graph of the function and perform the horizontal line test. Since no horizontal line intersects the graph more than once, the inverse of f is a function.

Finding the Inverse of a Radical Function

Verifying Functions are Inverses

Step 1: Find the inverse. The radius of the sphere is 5 ft.

Monitoring Progress

10) Yes 11) No