Lesson 1.7

Notes

Lesson 1.7 Inverse Functions and Graphing Inverse Functions Objectives: • Graph Piecewise Functions • Find inverse functions informally and verify that two functions are inverse functions of each other. • Use graph of functions to decide whether functions have inverse functions. • Determine whether functions are one-to-one. • Find inverse functions algebraically. Graph Piecewise Functions 1. A piecewise function is a function defined by two or more equations over a specified domain. Determine the equations and domain for the following piecewise function. Example 1: Graph f(x) = x2 + 1, when x < 0 and x – 1, when x ≥ 0. Find inverse functions informally and verify that two functions are inverse functions of each other. 2. An inverse function is a function that undoes the action of another function, by switching the two functions’ domain and range. Example: f(x) = x + 4, D: {1, 2, 3, 4}, R: {5, 6, 7, 8}. The inverse of f(x), denoted f-1(x) = x – 4, D: {5, 6, 7, 8}, R: {1, 2, 3, 4}. In the case of the inverse function, the domain of f must be equal to the range of f-1, and the range of f must be equal to the domain of f-1. 3. To verify two functions are inverses of each, get the compo...