University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 1 - Section 1.6 - Inverse Functions and Logarithms - Exercises - Page 48: 2

Answer

$y=x^4-x^2$ is not one-to-one.

Work Step by Step

*Condition for One-to-one Function (the Horizontal Line Test): The graph of function $y=f(x)$ intersects each horizontal line at most once. Looking at the graph of $y=x^4−x^2$, we notice that the graph would intersect a horizontal line more than once. In fact, I tried drawing a horizontal line $y=-\frac{1}{8}$. From the image below, you can see that $y=-\frac{1}{8}$ intersects our given graph at $4$ points. Therefore, we conclude that $y=x^4-x^2$ is not one-to-one.
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