If $f:[2, \infty) \rightarrow R$ is defined by $f(x)=x^2-4x+5$, then the range of $f$ is

The domain of definition of $f(x) = \sqrt{\frac{1-|x|}{2-|x|}}$ is: (Here $(a, b) = \{x : a < x < b\}$ and $[a, b] = \{x : a \leq x \leq b\}$)

Let $D$ be the domain of the function $f(x) = \sin^{-1} \left(\log_{3x} \left(\frac{6+2 \log_3 x}{-5x}\right)\right)$. If the range of the function $g: D \rightarrow R$ defined by $g(x) = x - [x]$ (where $[x]$ is the greatest integer function) is $(\alpha, \beta)$,then $\alpha^2 + \frac{5}{\beta}$ is equal to

If $f: R \rightarrow A$,defined by $f(x) = \cos x + \sqrt{3} \sin x - 1$,is an onto function,then $A =$

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

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