Questions in fun-lim

Select	Question
	The domain of the function $f(x)={{\sin }^{-1}}[{{\log }_{2}}(x/2)]$ is
	The domain of $f(x)=\frac{{{\log }_{2}}(x+3)}{{{x}^{2}}+3x+2}$ is
	The function $f(x)=\frac{{{\sec }^{-1}}x}{\sqrt{x-[x]}},$ where [.] denotes the greatest integer less than or equal to x is defined for all x belonging to
	If the domain of function $f(x)={{x}^{2}}-6x+7$ is $(-\infty ,\ \infty )$, then the range of function is
	The domain of the function $f(x)=\sqrt{\log \frac{1}{\|\sin x\|}}$ is
	The domain of the function $f(x)=\log (\sqrt{x-4}+\sqrt{6-x})$ is
	Domain of the function $f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}$ is
	The domain of the derivative of the function $f(x) = \begin{cases} {\tan ^{ - 1}}x\;\;\;\;\;,\;\|x\|\; \le 1\\ \frac{1}{2}(\|x\|\; - 1)\;,\;\|x\|\; > 1 \end{cases}$ is
	The domain of the function $f(x)={{\log }_{3+x}}({{x}^{2}}-1)$ is
	If ‘n’ is an integer, the domain of the function $\sqrt{\sin 2x}$ is