College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Review Exercises: 21

Answer

Odd

Work Step by Step

To find out if the function is even, odd, or neither, we find $f(−x)$ and compare the result to $f(x)$: $f(x)=\displaystyle \frac{x}{1+x^{2}}$ $\displaystyle f(-x)=\frac{-x}{1+(-x)^{2}}$ $\displaystyle =\frac{-x}{1+x^{2}}$ $=-\displaystyle \frac{x}{1+x^{2}}$ $=-f(x)$ Thus $f(x)$ is odd.
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