Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Section 1.3 Properties of Functions - 1.3 Assess Your Understanding - Page 75: 40

Answer

$\text{even}$

Work Step by Step

Recall: a) A function is said to be odd, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=-f(x)$ b) A function is said to be even, when every number $x$ in its domain, the number $-x$ is also in the domain such that $f(-x)=f(x)$ Replace $x$ with $-x$ to evaluate $f(-x)$: $f(-x)=\sqrt[3] {2(-x)^2+1} \\=\sqrt[3] {2x^2+1} \\=f(x)$ Therefore, the function $f(x)$ is even.
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