Relations and F...

Assertion(A):  If $$X=\left \{ x:-1\leq x\leq 1 \right \}$$  and  $$f:X\rightarrow X$$ defined by $$f(x)=\sin \pi x; \forall x\in A$$ is not invertible function

Reason (R): For a function $$f$$ to have inverse, it should be a bijection

Let $$S$$ be set of all rational numbers. The functions $$f:R\rightarrow R,\ g:R\rightarrow R$$ are defined as 
$$f(x)=\begin{cases}
0, & x \in S \\ 
1, & x \notin S
\end{cases}$$
$$g(x)=\begin{cases}
-1 & x\in S \\ 
 0 & x\notin S
\end{cases}$$
then, $$(fog) (\pi)+(gof)(e)=$$

If $$n\geq 1$$ is any integer, $$\mathrm{d}(n)$$ denotes the number of positive factors of $$n$$, then for any prime number $$\mathrm{p},\ \mathrm{d}(\mathrm{d}(\mathrm{d}(\mathrm{p}^{7})))=$$

Let $$\displaystyle f\left( x \right)={ x }^{ 2 }-x+1,x\ge \left( \frac { 1 }{ 2 }  \right) $$ then the solution of the equation $$f(x)=f^{-1}(x)$$ is

lf $$f:[-6,6]\rightarrow \mathbb{R}$$ is defined by $$f(x)=x^{2}-3$$ for $$x\in \mathbb{R}$$ then
$$(fofof)(-1)+(fofof)(0)+(fofof)(1)=$$

lf $$f$$ : $$R\rightarrow R$$ is defined by
$$f(x)=\left\{\begin{array}{l}x+4 & x<-4\\3x+2 & -4\leq x<4\\x-4 & x\geq 4\end{array}\right.$$
then the correct matching of list I to List II is. 

If $$f:R\rightarrow R$$ is defined by $$f(x)=x^{2}-10x+21 $$ then $$ f^{-1}(-3)$$ is

lf $$g(f(x)) =|\sin \mathrm{x}|,f(g(x)) =(\sin\sqrt{\mathrm{x}})^{2}$$, then

lf $$ f(x)=x-x^{2}+x^{3}-x^{4}+\ldots..\infty$$ when $$|x|<1$$, then the ascending order of the following is
a) $$f(1/2)$$
b) $$f^{-1}(1/2)$$
c) $$ f(-1/2)$$
d) $$f^{-1}(-1/2)$$

Let $$f$$ be an injective function with domain $$\{x, y, z\}$$and range $$\{1,2,3\}$$ such that exactly one of the follwowing statements is correct and the remaining are false :