Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises: 16

Answer

The graph of f fails the horizontal line test, so the function is not one-to-one on its domain, and therefore does not have 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 the graph of f FAILS the horizontal line test, (e.g. the horizontal line y=1 has more than one intersection with the graph of f) (it is sufficient to find one line wich causes the fail) the function is not one-to-one on its domain, and therefore does not have an inverse.
Small 1510592384
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.