Let $f:(-1,1) \rightarrow B$ be the function defined by $f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\righ

Question

Let $f:(-1,1) \rightarrow B$ be the function defined by $f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and such that it is a one-one and onto function. Then $B$ is

Professor PC Thomas Classes · Answer

Range of $\frac{2x}{1+x^2}$ for $x \in (-1, 1)$ is $(-1, 1)$. Thus, $\sin^{-1}$ maps this to $(-\frac{\pi}{2}