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Let $f : R \to R$ be defined by $f (x) = \frac{x}{1 + x^{2}}, x \in R .$ Then the range of $f$ is

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

$R - [- 1, 1]$

$[- \frac{1}{2}, \frac{1}{2}]$

$R - [- \frac{1}{2}, \frac{1}{2}]$

answer is C.

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$x \in R t h e n f (x) \in [\frac{- 1}{2}, \frac{1}{2}]$

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