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.