Relations and F...

Let $$\rho$$ be a relation defined on$$N$$, the set of natural numbers, as
$$\rho =\left\{ \left( x,y \right) \in N\times N:2x+y=41 \right\} $$ then

For real values of x ,the range of $$\frac {x^2+2x+1}{X^2+2x-1}$$ is

Let $$R = gS - 4$$. When $$S = 8, R = 16$$. When $$S = 10, R$$ is equal to

If $$f(g(x))=g(f(x))=x$$ for all real numbers $$x$$ and $$f(2)=5$$ and $$f(5)=3$$, then the value of $$g(3)+g(f(2))$$ is

The relation P defined from R to R as a P b $$\Leftrightarrow$$ 1 + ab > 0, for all a, b $$\epsilon$$ R is

If R is a relation on a finite set having n elements, then the number of relations on A is :

If $$f(x) = \dfrac {4x + x^{4}}{1 + 4x^{3}}$$ and $$g(x) = \ln \left (\dfrac {1 + x}{1 - x}\right )$$, then what is the value of $$f\cdot g \left (\dfrac {e - 1}{e + 1}\right )$$ equal to?

If the line $$x=\alpha$$ divides the area of the region $$R=\left\{(x,y)\in \mathbb{R}^2:x^3\le y\le x,0\le x\le 1\right\}$$ into two equal parts, then 

The period of the function 
$$f(x)=2^{\sqrt{\dfrac{2}{1-\cos 2x}}}+4^{\sqrt{\dfrac{1+\tan^2x}{4}}}$$