If` f(x+y)=f(x*y) `, `∀x,yϵR` and `f(2011)=2010` then `f(2012)=`

Let a real valued function f satisfy f(x + y) = f(x)f(y)AA x, y in R and f(0)!=0 Then g(x)=f(x)/(1+[f(x)]^2) is

Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k , then

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then f'(x)=

Let f(x) be a differentiable function satisfying f(y)f(x/y)=f(x) AA , x,y in R, y!=0 and f(1)!=0 , f'(1)=3 then

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

y=f(x), where f satisfies the relation f(x+y)=2f(x)+xf(y)+ysqrt(f(x)) , AAx,y->R and f'(0)=0.Then f(6)is equal ______

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let f(x) is a polynomial satisfying f(x).f(y) = f(x) +f(y) + f(xy) - 2 for all x, y and f(2) = 1025, then the value of lim_(x->2) f'(x) is