Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.2 One-to-One Functions; Inverse Functions - 4.2 Assess Your Understanding - Page 291: 30

Answer

The domain of the inverse function is given by: $\{2,6,8,−3,9\}$ The range of the inverse function is given by: $\{−2,−1,0,1,2\}$ The inverse function in the form of ordered pairs can be described as: $(2,−2),(6,−1),(8,0),(−3,1),(9,2)$

Work Step by Step

The inverse of a function interchanges a function's domain and range. This means that the domain of the inverse is the range of the original function, and vice-versa (the range of the inverse is the domain of the original function). Therefore, the inverse of the original function can be computed by switching the domain elements with the range elements. The domain of the inverse function is given by: $\{2,6,8,−3,9\}$ The range of the inverse function is given by: $\{−2,−1,0,1,2\}$ The inverse function in the form of ordered pairs can be described as: $(2,−2),(6,−1),(8,0),(−3,1),(9,2)$
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