Relations and F...

If $$f(x)=\dfrac{1}{2}(3^{x}+3^{-x}),  g(x)=\dfrac{1}{2}(3^{x}-3^{-x})$$  then $$ f(x)g(y)+f(y)g(x)$$ is equal to

If relation R$$=\left \{ (x,  x+2)  :  x  \in  N, 1 \leq  x <4 \right \}$$ then R is

If the range of function is $$\left [ \frac{5}{6},\frac{3}{2} \right ]$$, then the value of d is

If $$A=\{b,c,d\}$$ and $$B=\{x,y\}$$. Find which of the following are elements of $$A \times A$$.

The number of different solutions to the equation $$f (20x -11/ x) = 0$$ cannot be

Given $$A=\{b,c,d\}$$ and  $$B=\{x,y\}$$ : find element of  $$A\times B$$ .

Let $$f(x+y)=f(x) f(y) \forall x, y \in R, f(5) =2,  f'(0)=3$$, then $$f'(5)$$ equals:

If $$f(1)=1, f(n+1)=2f(n)+1,  n \geq 1$$, then $$f(n)$$ is:

n(A)=m and n(B)=n ; then