Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

$For-1<x<1,ta{n}^{-1}\frac{2x}{1-x^2}=2ta{n}^{-1}x$

Range of f(x) = $(-\frac{\pi }{2},\frac{\pi }{2}).$

$\therefore$ Co-domain of function = $(-\frac{\pi }{2},\frac{\pi }{2}).$