Section 7 7 Inverse Relations and Functions Inverse

Section 7. 7 Inverse Relations and Functions

Inverse of a Function f(x) = 2 x – 8 Input: 6 Multiply by 2 Subtract 8 Output: 4 g(x) = (x + 8)/2 Input: 4 Add 8 Divide by 2 Output: 6

Inverses and Their Coordinate Pairs �Graph the two functions on the same coordinate axes. �Find three points on the graph of f(x). �Reverse the coordinates of each point and then graph the new points. What do you notice?

Inverses and Their Coordinate Pairs

Inverse �Definition 1: If the graph of a function contains a point (a, b), then the graph of the inverse of a function contains the point (b, a).

Example 1: Finding an inverse function �Find the inverse of relation s. Graph s and its inverse. x 1 2 3 4 y -1 0 1 1 Inverse of s. x y

Example 2: Finding an inverse function �Find the inverse of relation s. Graph s and its inverse. x -1 0 1 2 y -2 -1 -1 -2 Inverse of s. x y

Inverses of Quadratics

Examples 3 – 6: Interchanging x and y �Find the inverse.

Example 3

Example 4

Example 5

Example 6

TOTD �Find the inverse of the function y = 4 x – 7.

Examples 7 – 10: Finding an Inverse Function. �Find the inverse.

Example 7

Example 8

Example 9

Example 10

TOTD �Find the inverse of f(x) = 4 x² - 2.

Property: Composition of Inverse Functions

Examples 11 – 13: Composition of Inverse Functions Find the inverses of the following functions, then prove that they are inverses.

Example 11

Example 12

Example 13

TOTD �If f(x) = 5 x + 8, find its inverse. Compose the function with its inverse and vice versa.