The range of $f(x)=4 \sin ^{-1}\left(\frac{x^2}{x^2+1}\right)$ is

Let ${f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R$ and $k \ge 1$, then ${f_4}\left( x \right) - {f_6}\left( x \right)$ is equal to

Let $E = \{ 1,2,3,4\} $ and $F = \{ 1,2\} $.Then the number of onto functions from $E$ to $F$ is

solve $\frac{{1 - \left| x \right|}}{{2 - \left| x \right|}} \ge 0$

Let $S=\{1,2,3,4,5,6,7\} .$ Then the number of possible functions $f: S \rightarrow S$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in S$ and $m . n \in S$ is equal to $......$

Range of the function $f(x) = {\sin ^2}({x^4}) + {\cos ^2}({x^4})$ is