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

The range of the real valued function $f(x) = \frac{1}{x - |x|}$ is

If $f: R \rightarrow R$ is defined by $f(x)=[2x]-2[x]$ for $x \in R$,where $[x]$ is the greatest integer not exceeding $x$,then the range of $f$ is:

Let $f: A \rightarrow B$ be defined as $f(x) = \frac{1}{2} - \tan \left(\frac{\pi x}{2}\right)$ and $g: B \rightarrow C$ be defined as $g(x) = \sqrt{3 + 4x - 4x^2}$. If $A, B, C$ are subsets of $\mathbb{R}$ and $f$ is an onto function,then the range of the function $f(x)$ 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):

The domain of the definition of the function $f(x) = \frac{1}{4 - x^2} + \log(x^3 - x)$ is