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

The domain of the function $f(x) = \sqrt{\log_e\left(\frac{1}{x^2-4x+4}\right)} + \sin^{-1}(x^2-2)$ is

$f(x)$ is a quadratic polynomial satisfying the condition $f(x) + f\left(\frac{1}{x}\right) = f(x) f\left(\frac{1}{x}\right)$. If $f(-1) = 0$,then the range of $f$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - [x] - 2}}$ is, where $[x]$ denotes the greatest integer function.

The range of the function $f(x) = -\sqrt{-x^2-6x-5}$ is

Let $[x]$ denote the greatest integer not more than $x$. If $A$ and $B$ are the domains of the functions $f(x)=\frac{x-[x]}{\sqrt{|x|-x}}$ and $g(x)=\frac{x-[x]}{\sqrt{|x|+x}}$ respectively, then