The domain of the function $f(x) = \sqrt{\cos x}$ is

If $n$ is an integer,the domain of the function $\sqrt{\sin 2x}$ is

Let $f:(1,3) \rightarrow R$ be a function defined by $f(x)=\frac{x[x]}{1+x^{2}},$ where $[x]$ denotes the greatest integer $\leq x.$ Then the range of $f$ is

If $f:[-3,2] \rightarrow [0, \sqrt[3]{x}]$ is an onto function defined by $f(n) = \begin{cases} 2+\sqrt[3]{n}, & -3 \leq n \leq -1 \\ n^{2/3}, & -1 < n \leq 2 \end{cases}$,then $x=$

Let the range of the function $f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, x \in \mathbb{R}$ be $[a, b]$. If $\alpha$ and $\beta$ are respectively the $A.M.$ and the $G.M.$ of $a$ and $b$,then $\frac{\alpha}{\beta}$ is equal to:

Find the range of the following function:
$f(x) = x^{2} + 2$,where $x$ is a real number.