Relations and F...

Find the domain of the function defined as $$f(x)=\dfrac{1}{1-x^2}$$.

If $$aN = (ax/x \ \epsilon \ N)$$ and $$bN \cap cN = dN,$$, where $$b, c \ \epsilon N$$ are relatively prime, then 

If $$f:R \to R$$ is a function satisfying $$f(x + y) = f(xy)$$ for all $$x, y \in R$$ and $$f\left(\dfrac{3}{4}\right) = \left( \dfrac{3}{4} \right)$$ , then $$f\left( \dfrac{9}{16} \right)$$ =

Find the domain of the function defined as $$f(x)=\dfrac{x+1}{2x+3}$$.

Let R be a relation from$$ A=\left\{ 1,2,3,4 \right\}  to B=\left\{ 1,3,5 \right\}$$  such that $$R=[(a,b):a<b,where\ a\epsilon A\ and\ b\epsilon B]$$. What is $$R$$ equal to?

$$x*y=\sqrt {\dfrac {(x+y)(y^{2}-12x)}{(x-2)(y-7)}}$$ then what will be the value of $$5*9$$?

If $$f:R \rightarrow S$$ defined by $$f(x)=\sin x-\sqrt {3} \cos x+1$$ is onto, then the interval of $$S$$ is 

If $$f:R\rightarrow R$$ is defined by $$ f\left( x \right) =\left| x \right| $$, then:

If $$f:\,R\, \to R\,$$ is an even function which is differentiable on R and $${f^N}\left( \pi  \right) = 1\,the\,{f^N}\left( { - \pi } \right)\,{\rm{is}}$$