Let the function


Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x}{1+x^{2}}$,

$x \in R$. Then the range of $f$ is :

  1. $(-1,1)-\{0\}$

  2. $\left[-\frac{1}{2}, \frac{1}{2}\right]$

  3. $\mathrm{R}-\left[-\frac{1}{2}, \frac{1}{2}\right]$

  4. $\mathrm{R}-[-1,1]$

Correct Option: , 2


$f(0)=0 \& f(\mathrm{x})$ is odd.

Further, if $x>0$ then

$f(x)=\frac{1}{x+\frac{1}{x}} \in\left(0, \frac{1}{2}\right]$

Hence, $f(\mathrm{x}) \in\left[-\frac{1}{2}, \frac{1}{2}\right]$

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