Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 1 - Functions - 1.1 Review of Functions - 1.1 Exercises: 96

Answer

The function is odd.

Work Step by Step

We have that $\mathbb{E}(-x)=\mathbb{E}(x)$ and $\mathbb{O}(-x)=-\mathbb{O}(x)$. Let $\Phi=\mathbb{E}\cdot \mathbb{O}$. Then $$\Phi(-x)=\mathbb{E}(-x)\cdot\mathbb{ O}(-x)=\mathbb{E}(x)\cdot(-\mathbb{O}(x))=-\mathbb{E}(x)\mathbb{O}(x)=-\Phi(x)$$ which means that this function is odd.
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