The domain of the function given by $2^x+2^y=2$ is

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

The domain of definition of the function $y(x)$ given by the equation $2^x+2^y=2$ is

If $[x]$ represents the greatest integer $\leq x$, then the range of the real-valued function $f(x) = \frac{1}{\sqrt{[x]^2+[x]-2}}$ 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

If $f$ is a real-valued function from $A$ onto $B$ defined by $f(x) = \frac{1}{\sqrt{|x - |x||}}$, then $A \cap B = $