## Discrete Mathematics with Applications 4th Edition

$g(x)=\frac{2x^{3}+2x}{x^{2}+1}=\frac{(2x)(x^{2}+1)}{x^{2}+1}=2x=f(x)$ Yes, the functions $f$ and $g$ are equivalent.
Note that $x^{2}+1\ne0$; therefore, $g$ has the same domain as $f$.