Relations Test ...

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 $$5*9$$?

Let $$R$$ be a reflexive relation in a finite set having $$n$$ elements and let there be $$m$$ ordered pairs in $$R$$. Then,

Let S be a non-empty set. Let R be a relation on P(S), defined as ARB$$\Leftrightarrow A\cap B\neq \phi$$. The relation R is?

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

Let R be a relation from N to N defined by 
$$R = \left\{ {\left( {a,\,b} \right):a,\,b\, \in \,N\,\,and\,\,a = {b^2}} \right\}$$

Let $$A = \left\{ {a,\,b,\,c} \right\}$$ and $$B = \left\{ {4,\,5} \right\}$$. Consider a relation defined from set A to set B, then R is equal to

If $$A = \{2, 3, 5\}$$ and $$B = \{5, 7\}$$, find the set with highest number of elements:

If $$f:R \to R$$ is defined by $$f\left( x \right) = {x^2} - 3x + 2$$ and $$f\left( {{x^2} - 3x - 2} \right) = a{x^4} + b{x^3} + c{x^2} + dx + e$$ then $$a + b + c + d + e = $$