Chapter 6: Radical functions and rational exponents Section 6.7: Inverse Relations and functions

Section 6.7: Inverse relations and functions Goal: To find the inverse of a relation or function

Section 6.7: Inverse relations and functions Inverse Relation: obtained by interchanging the first and second coordinates in every pair of the original relation i.e. the domain for the inverse is the range for the original…the range for the inverse is the domain for the original

Section 6.7: Inverse relations and functions Example 1. Find the inverse of the function {(1, 1), (1.5, 1), (2, 2), (2.5, 2)}. State the domain and range of this inverse. Determine if the inverse is a function.

Section 6.7: Inverse relations and functions Inverse function: if f is the function, then its inverse is denoted by f-1 One-to-one correspondence: when both the original and the inverse are functions To find the inverse function, switch the x and y variables

Section 6.7: Inverse relations and functions Examples: 2. Find the inverse of the function and determine if the inverse is also a function. Graph f, f-1, and y = x on the same coordinate plane.

Section 6.7: Inverse relations and functions Examples: What is f-1 if f(x) = . Find f-1(7)

Section 6.7: Inverse relations and functions Examples: If f(x) = 8x + 1, what is f(f-1(4)) and f-1(f(-3)) What is f-1(f(x)) and f(f-1(x))

Section 6.7: Inverse relations and functions Examples Give five points on f-1(x) if f(x) = -2x2 – 3 What is f-1(-13) if f(x) = -6x + 11

Section 6.7: Inverse relations and functions Examples: What is the domain and range of f-1(x) if f(x)= -4|9+5x| + 3

Section 6.7: Inverse relations and functions Graph the inverse for the following graph (-6, 3) (5, 2) (0, 0) (-2, -1)

Section 6.7: Inverse relations and functions Homework: Pg. 410 #8-40 (even)