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

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

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

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

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

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

Solution

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