JEE Math Practice Question

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

1. A.$$\left( {0,{\pi \over 2}} \right)$$
2. B.$$\left[ {0,{\pi \over 2}} \right)$$
3. C.$$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$
4. D.$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$