Questions in fun-lim

Select	Question
	Let $f(x)=ax+b$ and $g(x)=cx+d,\ a\ne 0,\ c\ne 0$. Assume $a=1,\ b=2$. If $(fog)(x)=(gof)(x)$ for all x, what can you say about c and d
	Let $g(x)=1+x-[x]$ and $f(x) = \begin{cases} - 1,\;x {\rm{0}} \end{cases}$ then for all $x,\ f(g(x))$ is equal to
	If $f(x)=\frac{\alpha \,x}{x+1},\ x\ne -1$. Then, for what value of $\alpha $ is $f(f(x))=x$
	If $f(x)=\frac{2x+1}{3x-2}$, then $(fof)(2)$ is equal to
	If $f(x)={{\sin }^{2}}x$ and the composite function $g\{f(x)\}=\|\sin x\|$, then the function $g(x)$ is equal to
	If $f(x)={{(a-{{x}^{n}})}^{1/n}},$where $a>0$and n is a positive integer, then $f[f(x)]=$
	Let $f:(-1,1)\to B$, be a function defined by $f(x)={{\tan }^{-1}}\frac{2x}{1-{{x}^{2}}},$ then f is both one- one and onto when B is the interval
	A real valued function $f(x)$ satisfies the function equation $f(x-y)=f(x)f(y)-f(a-x)f(a+y)$ where a is a given constant and $f(0)=1$, $f(2a-x)$ is equal to
	If X and Y are two non- empty sets where $f:X\to Y$is function is defined such that $f(c)=\left\{ f(x):x\in C \right\}$for $C\subseteq X$and ${{f}^{-1}}(D)=\{x:f(x)\in D\}$for $D\subseteq Y$ for any $A\subseteq X$ and $B\subseteq Y,$then
	If $f(x)=2{{x}^{6}}+3{{x}^{4}}+4{{x}^{2}}$ then $f'(x)$ is