The function $f(x) = \operatorname{sech}(x)$ on $R$ has the range

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

The domain of the real-valued function $f(x) = \frac{\sqrt{\log_{10}\left(\frac{x}{x-2}\right)}}{\sqrt{[x]^2-5[x]+6}}$ is (where $[x]$ denotes the greatest integer function):

If a relation $R$ on the set of natural numbers $N$ is defined by $x + 2y = 8$,then the domain of $R$ is:

Domain of $y = \sqrt{\log _{10} \frac{3x - x^2}{2}}$ is

If $f: R \rightarrow A$ defined by $f(x) = \frac{1}{x^2+2x+2}$,$\forall x \in R$ is surjective,then $A =$