The function $f: R \to \bigg[ -\large\frac{1}{2} ,\frac{1}{2} \bigg]$ defined as $f(x) = \large\frac{x}{1+x^2}$ is

Question

$\begin{array}{1 1} \text{(1) injective but not surjective.} \\ \text{(2) surjective but not injective.} \\ \text{(3) neither injective nor surjective.} \\ \text{ (4) invertible.}\end{array}$