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