## Calculus 10th Edition

Published by Brooks Cole

# Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 343: 20

#### Answer

the graph of f passes the horizontal line test, the function is one-to-one on its domain, and therefore has an inverse.

#### Work Step by Step

The Horizontal Line Test is discussed on p.339, between Theorems 5.6 and 5.7. Graph the function. Also, graph several horizontal lines to illustrate whether all horizontal lines intersect the graph at most once. If this is so, the graph passes the Horizontal line test. If not (if there is a horizontal line with two or more intersections), the graph fails the test. The screenshot below shows that, since a horizontal line either does not intersect the graph (such as $y=-1)$, or if it does, it does at most once, the graph of f passes the horizontal line test, the function is one-to-one on its domain, and therefore has an inverse.

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