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

The domain of the function $f(x) = \sqrt{\frac{x}{1+x}}$ is

The domain of the function $f(x) = \sqrt{x-1} + \sqrt{6-x}$ is...

If $R-(\alpha, \beta)$ is the range of $\frac{x+3}{(x-1)(x+2)}$,then the sum of the intercepts of the line $\alpha x+\beta y+1=0$ on the coordinate axes is

The domain of the function $f(x) = \sqrt{\frac{x-7}{9-x}}$ is

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