The function $f : R \to \begin{bmatrix}-\frac{1}{2}, \frac{1}{2} \end{bmatrix}$ defined as $f(x) = \frac{x}{1+x^2}$, is :

Question

( A ) surjective but not injective
( B ) Invertible
( C ) injective but not surjective
( D ) neither injective nor surjective