Let $ f : (-1, 1) \to B$ be a function defined by$f(x) = \tan^{-1} \frac{2x}{1-x^2}$, then $f$ is both one-one and onto when $B$ is the interval :

Question

( A ) $ \begin{pmatrix} -\frac{\pi}{2}, \frac{\pi }{2} \end{pmatrix}$
( B ) $[ 0 , \frac{\pi}{2} )$
( C ) $ \begin{bmatrix} -\frac{\pi}{2}, \frac{\pi }{2} \end{bmatrix}$
( D ) $ \begin{pmatrix} 0, \frac{\pi }{2} \end{pmatrix}$