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

If $[x]$ denotes the greatest integer $\leq x$,then the domain of the function $f(x)=\sqrt{\frac{4-x^2}{[x]+2}}$ is

The domain of the function $f(x) = \log (\sqrt {x - 4} + \sqrt {6 - x} )$ is

If $f: R \rightarrow R$ is defined by $f(x) = \frac{1}{2 - \cos 3x}$ for each $x \in R$,then the range of $f$ is

Find the domain and range of the following real function:
$f(x) = \sqrt{9 - x^{2}}$

The largest interval lying in $\left( -\frac{\pi}{2}, \frac{\pi}{2} \right)$ for which the function $f(x) = 4^{-x^2} + \cos^{-1}\left( \frac{x}{2} - 1 \right) + \log(\cos x)$ is defined is: