The interval in which the curve represented by $f(x)=2 x+\log \left(\frac{x}{2+x}\right)$ is

The set of real values of $x$ such that $f(x)=\sqrt{\frac{[x]-1}{\left.[x]^2-[x]-6\right]}}$ is a real valued function is

If a function $f: Z \rightarrow Z$ is defined by $f(x)=x-(-1)^x$, then $f(x)$ is

Domain of the real valued function $f(x)=\log \left(x^2-1\right)+x \operatorname{coth}^{-1} x$ is