The domain of $f(x) = \frac{1}{{\sqrt {{{\log }_{\frac{\pi }{4}}}({{\sin }^{ – 1}}x) – 1} }}$,is

Range of the function , $f (x) = cot ^{-1}$ $\left( {{{\log }_{4/5}}\,\,(5\,{x^2}\,\, – \,\,8\,x\,\, + \,\,4)\,} \right)$ is :

The domain of the derivative of the function $f(x) = \left\{ \begin{array}{l}{\tan ^{ – 1}}x\;\;\;\;\;,\;|x|\; \le 1\\\frac{1}{2}(|x|\; – 1)\;,\;|x|\; > 1\end{array} \right.$ is

If domain of function $f(x) = \sqrt {\ln \left( {m\sin x + 4} \right)} $ is $R$ , then number of possible integral values of $m$ is

Let $f : R \rightarrow R$ be a function such that $f(x)=\frac{x^2+2 x+1}{x^2+1}$. Then