Domain of the definition of function 

$f(x) = \sqrt {\frac{{4 – {x^2}}}{{\left[ x \right] + 2}}} $ is      $($ where $[.] \rightarrow G.I.F.)$

Statement $1$ : If $A$ and $B$ be two sets having $p$ and $q$ elements respectively, where $q > p$. Then the total number of functions from set $A$ to set $B$ is $q^P$.
Statement $2$ : The total number of selections of $p$ different objects out of $q$ objects is ${}^q{C_p}$.

Let $x$ be a non-zero rational number and $y$ be an irrational number. Then $xy$ is

The graph of $y = f(x)$ is shown then number of solutions of the equation $f(f(x)) =2$ is

Let ${a_2},{a_3} \in R$ such that $\left| {{a_2} – {a_3}} \right| = 6$ and $f\left( x \right) = \left| {\begin{array}{*{20}{c}}
1&{{a_3}}&{{a_2}}\\
1&{{a_3}}&{2{a_2} – x}\\
1&{2{a_3} – x}&{{a_2}}
\end{array}} \right|,x \in R.$ Then the greatest value of $f(x)$ is