Relations and F...

If $$f(x)=2x-1, g(x)=x^{2} $$ then $$ (3f-2g)(x)=$$

If $$f(x)$$ is a polynomial in $$x(>0)$$ satisfying the equation $$ f(x)+f\left (\dfrac1x\right)=f(x).f\left (\dfrac1x\right)$$ and $$f(2)=-7$$,  then $$f(3)$$ is equal to

If $$f(x+y)=f(x)f(y)$$  and  $$f(5)=32$$  then  $$f(7)=$$

If a non-zero function $$f$$ satisfies the relation $$f(x+y)+f(x-y)=2f(x).f(y)$$ for all $$x, y$$ in $$R$$ and $$f(0) \neq 0$$; then $$f(10)-f(-10)=$$

If relation $$R$$ is defined by $$\mathrm{R}=\{(\mathrm{x},\ \mathrm{y}):2\mathrm{x}^{2}+3\mathrm{y}^{2}\leq 6\}$$, then the domain of $$\mathrm{R}$$ is

The domain and range of relation $$R=\{(x,y) | x, y \in N$$, $$x+2y=5\} $$ is?

If $$R$$ is the relation 'less than' from $$A=\{1, 2, 3, 4, 5\}$$ to $$B=\{1, 4\}$$, the set of ordered pairs corresponding to $$R$$, then the inverse of $$R$$ is

If $$A$$ is the set of even natural numbers less than $$8$$ and $$B$$ is the set of prime numbers less than $$7$$, then the number of relations from $$A$$ to $$B$$ is

The range of the function $$f(x)=\dfrac{\sin(\pi [x])}{x^{2}+1}$$ (where $$[.]$$ denotes greatest integer function) is

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