Answer
Even
Work Step by Step
To find out if the function is even, odd, or neither, we find $g(−x)$ and compare the result to $g(x)$:
$g(x)=\displaystyle \frac{4+x^{2}}{1+x^{4}}$
$\displaystyle g(-x)=\frac{4+(-x)^{2}}{1+(-x)^{4}}$
$\displaystyle =\frac{4+x^{2}}{1+x^{4}}$
$\displaystyle =g(x)$
Thus $g(x)$ is even.
