Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.2 One-to-One Functions; Inverse Functions - 5.2 Assess Your Understanding - Page 266: 30

Answer

The domain of the inverse function will be: $\{5.0,8.5,6.7,5.5\}$. The range of the inverse function will be: $\{\text{Virginia}, \text{Nevada}, \text{Tennessee}, \text{Texas}\}$. The inverse function will create the following ordered pairs: $(5.0,\text{Virginia}), (8.5,\text{Nevada}), (6.7,\text{Tennessee}),( 5.5,\text{Texas}).$

Work Step by Step

In case of a one-to-one function, the inverse’s domain will be the original function’s range and the inverse’s range will be the original function’s range. The domain of the inverse function will be: $\{5.0,8.5,6.7,5.5\}$. The range of the inverse function will be: $\{\text{Virginia}, \text{Nevada}, \text{Tennessee}, \text{Texas}\}$. The inverse function will create the following ordered pairs: $(5.0,\text{Virginia}), (8.5,\text{Nevada}), (6.7,\text{Tennessee}),( 5.5,\text{Texas}).$
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