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