A) \[\left( 0,\frac{\pi }{2} \right)\]
B) \[\left[ 0,\frac{\pi }{2} \right)\]
C) \[\left[ -\frac{\pi }{2},\frac{\pi }{2} \right]\]
D) \[\left( -\frac{\pi }{2},\frac{\pi }{2} \right)\]
Correct Answer: D
Solution :
\[x\in (-1,1)\Rightarrow {{\tan }^{-1}}x\in \left( -\frac{\pi }{4},\frac{\pi }{4} \right)\] \[\Rightarrow \] \[2{{\tan }^{-1}}x\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] and \[f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}}=2{{\tan }^{-1}}x,({{x}^{2}}<1)\] \[\therefore \] \[f(x)\in \left( -\frac{\pi }{2},\frac{\pi }{2} \right)\] Function is one-one onto.
You need to login to perform this action.
You will be redirected in
3 sec
