Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter 4 - Inverse, Exponential, and Logarithmic Functions - 4.1 Inverse Functions - 4.1 Exercises - Page 416: 25


not one-to-one

Work Step by Step

A function $f$ is a one-to-one function if different values of the domain correspond to different values of the range. ---------- When we see $($... x ...$)^{2}$ in the function expression, our first thought should be "this is probably not one-to-one", because, for example, $1^{2}=(-1)^{2}$... We can get 1 in the parentheses if x=0 and $-1$ if $x=-2. $ So, for two different values from the domain, $0$ and $-2$... $f(0)=2(1)^{2}-6=-4$ $f(-2)=2(-1)^{2}-6=-4$ ... we have the same function value.
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