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 [AIEEE 2005]

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

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

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

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

Let \[f:(-1,1)\to B\], be a function defined by \[f(x)={{\tan }^{-1}}\

1.	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 [AIEEE 2005]
A.	\[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]
B.	\[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
C.	\[\left( 0,\frac{\pi }{2} \right)\]
D.	\[\left[ 0,\frac{\pi }{2} \right)\]
Answer» C. \[\left( 0,\frac{\pi }{2} \right)\]

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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 [AIEEE 2005]

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