Answer
Even
Work Step by Step
Remember that when a function is odd, then $g(−x)=−g(x)$ and when a function is even, then $g(−x)=g(x)$.
Thus, in order to find out whether the function is even, odd, or neither, we will find $g(-x)$ .
We are given:
$g(x)=\dfrac{4+x^2}{1+x^4}$
Thus, we have:
$g(-x)=\dfrac{4+(-x)^2}{1+(-x)^4} \\ = \dfrac{4+x^2}{1+x^4} \\= g(x)$
This shows that the function $g(x)$ is even.
