Relations and F...

If $$R$$ is a relation on the set $$A=\left\{ 1,2,3,4,5,6,7,8,9 \right\} $$ given by $$xRy\Leftrightarrow y=3x$$, then $$R=$$

A is a set having $$6$$ distinct elements. The number of distinct function from A to A which are not bijections is?

If $$f(x) = log_e \left(\dfrac{1 - x}{1 + x} \right) $$ then $$f \left(\dfrac{2x}{1 + x^2} \right)$$ is equal to 

The number of ordered pairs (a, b) of positive integers such that $$\dfrac{2a - 1}{b}$$ and $$\dfrac{2b - 1}{a}$$ are both integers is 

Let $$f : \rightarrow $$ satisfy $$f(x) f(y) = f(xy)$$ for all real numbers x and y. If $$f(2) = 4$$ then $$f\left(\dfrac{1}{2} \right) = $$

For all rest numbers $$x$$ and $$y$$, it is known as the real valued function $$f$$  satisfies $$f(x) +f(y) = f(x+y)$$. If $$f(1) = 7$$. then $$\displaystyle \sum_{r=1}^{100} f(r)$$ is equal to

If $$f(x) = \dfrac{1}{x^2 + 4x + 4} - \dfrac{4}{x^4 + 4x^2 + 4x^2} + \dfrac{4}{x^3 + 2x^{2'}}$$ then $$f\left(\dfrac{1}{2}\right)$$ is equal to

If $$A=\{x\in R:x^2-5|x|+6=0\}$$, then $$n(A)=$$ ________.

If $$f(x)=3x-2$$ and $$g(x)=x^2$$, then $$fog(x)=$$_______.

Let $$f: (-1, 1) \rightarrow (-1, 1)$$ be continuous , $$f(x) = f(x^2)$$ for all $$x \in (-1, 1)$$ and $$f(0) = \dfrac{1}{2}$$ , then the value of $$4 f \left(\dfrac{1}{4} \right)$$ is