#### Answer

the function f is an odd function

#### Work Step by Step

Calculate $f(t)$ and $f(-t)$
$f(t)=\frac{t}{t^{2}+1}$
$f(-t)=\frac{-t}{(-t)^{2}+1}=-\frac{t}{t^{2}+1}$
therefore we can see that the function f is an odd function that satisfies $f(-x)=-f(x)$ for every x in the domain.