If $\phi (x) = {a^x}$, then ${\{ \phi (p)\} ^3} $ is equal to

Domain of the definition of function 

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

Domain of the function $f(x) = \frac{{{x^2} - 3x + 2}}{{{x^2} + x - 6}}$ is

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

Let $f ( x )=2 x ^{ n }+\lambda, \lambda \in R , n \in N$, and $f (4)=133$, $f(5)=255$. Then the sum of all the positive integer divisors of $( f (3)- f (2))$ is

The period of the function $f(x) = \log \cos 2x + \sin 4x$ is :-