Relations and F...

Let $$R$$ be a relation such that $$R = \{(1,4), (3, 7), (4, 5), (4, 6), (7, 6) \}$$ then $$(R^{-1} oR)^{-1} =$$

The population of a town increases by $$5\%$$ every year. If the present population is $$5,40,000$$  find the population after 2 years. 

If $$f(x+y)=2f(x)\times f(y)$$, $$f$$ is differentiable and $$f(2)=8$$ then $$f'(3)$$ equals

Find x and y, if $$(x+3,5)=(6,2x+y)$$.

If $$f\left( {\sqrt {\left( {\dfrac{{x - 1}}{{x + 1}}} \right)} } \right) = 3x,$$ then the value of $$f\left( 3 \right)$$ is :

The function $$f\left( x \right) = \log x - \dfrac{{2x}}{{2 + x}}$$ is increasing in the interval 

A relation $$R$$ is defined from $$\left\{ 2,3,4,5 \right\} $$ to $$\left\{ 3,6,7,10 \right\} $$ by:

Let $$R$$ be a relation on the set $$N$$ given by $$R=\left\{ \left( a,b \right) :a=b-2,b>6 \right\}$$. Then

If $$A=\left\{ 1,2,3 \right\} , B=\left\{ 1,4,6,9 \right\} $$ and $$R$$ is a relation from $$A$$ to $$B$$ defined by $$x$$ is greater than $$y$$. The range of $$R$$ is

A relation $$\phi$$ from $$C$$ to $$R$$ is defined by $$x\phi y\Leftrightarrow \left| x \right| =y$$. Which one is correct?