Relations and F...

Let $$R$$ be a relation on $$N$$ defined by $$x+2y=8$$. The domain of $$R$$ is

If y is a function of x and $$\log (x + y) = 2xy$$, then the value of y'(0) = .....

If $$f(x+y)=f(x)f(y)$$ and $$ \sum^{\infty}_{x=1}f(x)=2\,x\,y\epsilon N$$, where $$N$$ is the set of all natural number, then the value of $$f(4)/f(2)$$ is:

If $$\displaystyle f(x)= \cos{ \left[ \pi ^{ 2 } \right] x}+ \cos{( \left[ -\pi ^{ 2 } \right]x)}$$, where $$[.]$$ denotes the step function, then

Let $$A$$ be a non-empty set such that $$A \times A$$ has $$9 $$ elements among which are found $$(-1, 0)$$ and $$(0, 1)$$, then

If $$\displaystyle f(a)=\log\left ( \frac{2+a}{2-a} \right ), 0< a<2$$ then $$ \displaystyle \frac{1}{2}f\left ( \frac{8a}{4+a^{2}} \right )=$$  

If $$f(x)=ax+\beta $$  and $$ f=\left \{ (1,1),(2,3),(3,5),(4,7) \right \} $$ then the values of $$ \alpha$$ and $$\beta $$ are 

If $$f(x)=2^{x}$$ then $$\dfrac{f(x+3)}{f(x-1)}=$$

$$ f \left ( x +\dfrac{1}{x} \right ) = x^{2} + \dfrac{1}{x^{2}} $$

$$f:R\rightarrow R$$ is defined as $$f(x)=2x+\left | x \right |$$ then $$f(2x)-f(-x)-4x=$$