Question:
Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^{2}}$,
$x \in R$. Then the range of $f$ is :
Correct Option: , 2
Solution:
$f(0)=0 \& f(\mathrm{x})$ is odd.
Further, if $x>0$ then
$f(x)=\frac{1}{x+\frac{1}{x}} \in\left(0, \frac{1}{2}\right]$
Hence, $f(\mathrm{x}) \in\left[-\frac{1}{2}, \frac{1}{2}\right]$