Domain of the function $f(x) = {\sin ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\cos ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right) + {\tan ^{ - 1}}\left( {\frac{{2 - |x|}}{4}} \right)$ is

Let $R =\{ a , b , c , d , e \}$ and $S =\{1,2,3,4\}$. Total number of onto function $f: R \rightarrow S$ such that $f(a) \neq$ 1 , is equal to $.............$.

The range of the function $f(x){ = ^{7 - x}}{\kern 1pt} {P_{x - 3}}$ is

If $f(x + ay,\;x - ay) = axy$, then $f(x,\;y)$ is equal to

For $x\,\, \in \,R\,,x\, \ne \,0,$ let ${f_0}(x) = \frac{1}{{1 - x}}$ and ${f_{n + 1}}(x) = {f_0}({f_n}(x)),$ $n\, = 0,1,2,....$  Then the value of ${f_{100}}(3) + {f_1}\left( {\frac{2}{3}} \right) + {f_2}\left( {\frac{3}{2}} \right)$ is equal to

Let $A=\{a, b, c\}$ and $B=\{1,2,3,4\}$ Then the number of elements in the set $C =\{ f : A \rightarrow B \mid 2 \in f ( A )$ and $f$ is not one-one $\}$ is