Questions in fun-lim

Select	Question
	If $f(x)=\frac{\alpha x}{x+1},x\ne -1$, for what value of $\alpha $ is $f(f(x))=x$
	Function $f(x)=x-[\,],$ where [ ] shows a greatest integer. This function is
	Let $g(x)=1+x-[x]$ and $f(x) = \begin{cases} - 1,\,\,\,If\,\,x 0 \end{cases}$ then for all values of x the value of $fog(x)$
	If $g:[-2,\,2]\to R$where $g(x)=$ ${{x}^{3}}+\tan x+\left[ \frac{{{x}^{2}}+1}{P} \right]$is a odd function then the value of parametric P is
	The Domain of function $f(x)={{\log }_{e}}(x-[x])$ is
	The domain of ${{\sin }^{-1}}({{\log }_{3}}x)$ is
	If $f({{x}_{1}})-f({{x}_{2}})=f\left( \frac{{{x}_{1}}-{{x}_{2}}}{1-{{x}_{1}}{{x}_{2}}} \right)$ for ${{x}_{1}},{{x}_{2}}\in [-1,\,1]$, then $f(x)$ is
	If equation of the curve remain unchanged by replacing x and y from –x and –y respectively, then the curve is
	If equation of the curve remain unchanged by replacing x and y from y and x respectively, then the curve is
	A condition for a function $y=f(x)$ to have an inverse is that it should be