If $\mathrm{f}:[1, \infty) \rightarrow[2, \infty)$ is given by $\mathrm{f}(x)=x+\frac{1}{x}$ then $\mathrm{f}^{-1}(x)$ equals

If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

Let $\mathrm{f}(x)=\frac{a x}{x+1}, x \neq-1$, then for $\alpha=$ ________, $\mathrm{f}(\mathrm{f}(x))=x$.

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