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

A

$$\left(0, \frac{\pi}{2}\right)$$

B

$$\left[0, \frac{\pi}{2}\right)$$

C

$$\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$$

D

$$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$