Relations and F...

If $$f\left( x \right) =\begin{cases} 2+x,\quad x\ge 0 \\ 2-x,\quad x<0 \end{cases}$$ then $$f\left( f\left( x \right)  \right) $$ is given by

Let $$f:X \to \left[ {1,\,27} \right]$$ be  a function by $$f\left( x \right) = 5\sin x + 12\cos x + 14$$. The set $$X$$ so that $$f$$ is one-one and onto is 

If : $$f(x) = 5 {x}^{2}$$, $$g(x) = 3x^{4}$$, then : $$(fog) (-1) =$$ 

For $$a,\ b\ \in \ R-\left\{ 0 \right\}$$, let $$f(x)=ax^{2}+bx+a$$ satisfies $$f\left(x+\dfrac{7}{4}\right)=f\left(\dfrac{7}{4}-x\right) \forall \ x\ \in\ R$$.
Also the equation $$f(x)=7x+a$$ has only one real distinct solution. The minimum value of $$f(x)$$ in $$\left[0,\dfrac{3}{2}\right]$$ is equal to

If $$f\left( x \right) = (1 - x)$$ , $$x \in \left[ { - 3,3} \right]$$ , then the domain of $$f\left( {f\left( x \right)} \right)$$ is

If f(g(x))=5x+2 and g(x)=8x then f(x)=

Let $$g\left( x \right) =1+x-\left[ x \right] $$ and $$f\left( x \right) =\begin{cases} -1,x<0 \\ 0,x=0 \\ 1,x>0 \end{cases}$$ Then for all $$x,f\left( g\left( x \right) \right) $$ is equal to (where $$\left[ . \right] $$ represents the greatest integer function)

If $$f:R \rightarrow R, f(x)=2x-1$$ and $$g; R \rightarrow R, g(x)=x^{2}+2$$, then $$(gof)(x)$$ equals-

Let $$g(x)=1+x-[x]\quad $$ and $$f(x)=\begin{cases} -1\quad if\quad x<0 \\ 0\quad \quad if\quad x=0 \\ 1\quad \quad if\quad x>0 \end{cases}$$ , then $$\forall \:x,fog(x)$$ equals 

The last three digits, if $$(12345956)_{10}$$ is expressed in binary system.