The domain of the function $y=f(x)$,where $x$ and $y$ are related by $2^x+2^y=2$ is

Let $f : R \rightarrow R$ be a function defined by $f(x) = \log_{\sqrt{m}}\{\sqrt{2}(\sin x - \cos x) + m - 2\}$,for some $m$,such that the range of $f$ is $[0, 2]$. Then the value of $m$ is $............$

The range of the function $f(x)=\sin [x]$,where $-\frac{\pi}{4} < x < \frac{\pi}{4}$ and $[x]$ denotes the greatest integer $\leq x$,is

The domain of $f(x) = \sqrt{\left(\frac{1}{\sqrt{x}} - \sqrt{x+1}\right)}$ is

The range of the function $f(x) = \frac{x}{x^2 - 5x + 9}$ is

The domain of the function $f(x) = \frac{1}{\sqrt{[x]^2 - [x] - 2}}$ is,where $[x]$ denotes the greatest integer function.