The period of the function $f (x) =$$\frac{{|\sin x| + |\cos x|}}{{|\sin x - \cos x|}}$  is

Suppose $f:[2,\;2] \to R$ is defined by $f(x) = \left\{ \begin{array}{l} - 1\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{for}}\; - 2 \le x \le 0\\x - 1\;\;\;\;\;{\rm{for}}\;0 \le x \le 2\end{array} \right.$, then $\{ x \in ( - 2,\;2):x \le 0$ and $f(|x|) = x\} = $

If $f(x) = \frac{{\alpha \,x}}{{x + 1}},\;x \ne - 1$. Then, for what value of $\alpha $ is $f(f(x)) = x$

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

If the domain of the function $f(x)=\sec ^{-1}\left(\frac{2 x}{5 x+3}\right)$ is $[\alpha, \beta) \cup(\gamma, \delta]$, then $|3 \alpha+10(\beta+\gamma)+21 \delta|$ is equal to $.......$.

The domain of the function

$f(x)=\frac{\cos ^{-1}\left(\frac{x^{2}-5 x+6}{x^{2}-9}\right)}{\log _{e}\left(x^{2}-3 x+2\right)} \text { is }$