The domain of the real valued function $f(x) = \sqrt{2+x} + \sqrt{3-x}$ is

The domain of the real valued function $f(x) = \sqrt{9 - \sqrt{x^2 - 144}}$ is

Let $R$ be the set of real numbers and $f: R \rightarrow R$ be given by $f(x) = \sqrt{|x|} - \log(1 + |x|)$. We now make the following assertions:
$I.$ There exists a real number $A$ such that $f(x) \leq A$ for all $x$.
$II.$ There exists a real number $B$ such that $f(x) \geq B$ for all $x$.

Find the domain of the function $f(x) = \frac{x^{2}+2x+1}{x^{2}-8x+12}$.

The set of all real values of $x$ for which $f(x)=\sqrt{\frac{|x|-2}{|x|-3}}$ is a well-defined function is

If $f(x) = [x]^{2} - 5[x] + 6 = 0$,where $[x]$ denotes the greatest integer function,then $x \in$