#### Answer

$g(x)=\frac{2x^{3}+2x}{x^{2}+1}=\frac{(2x)(x^{2}+1)}{x^{2}+1}=2x=f(x)$
Yes, the functions $f$ and $g$ are equivalent.

#### Work Step by Step

Note that $x^{2}+1\ne0$; therefore, $g$ has the same domain as $f$.

Published by
Cengage Learning

ISBN 10:
0-49539-132-8

ISBN 13:
978-0-49539-132-6

Note that $x^{2}+1\ne0$; therefore, $g$ has the same domain as $f$.

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