Find the domain of the function $f(x) = \frac{x^{2}+2x+1}{x^{2}-8x+12}$.

The domain of the function $f(x) = \sqrt{x - x^2} + \sqrt{4 + x} + \sqrt{4 - x}$ 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:

The domain of the function $f(x) = \log (\sqrt {x - 4} + \sqrt {6 - x} )$ 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 $............$

Which one of the following best represents the graph of $y = \frac{|x-x^2|}{x^2-x}$?