If `f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1,` then find the value of `f(7)dot`

If f(x+f(y))=f(x)+y for all x,y in R and f(1)=1, then find the value of f(10)/5,f(x) is not constant function.

If f(x+ y) = f(x) + f(y) for x, y in R and f(1) = 1, then find the value of lim_(x->0)(2^(f(tan x)-2^f(sin x)))/(x^2*f(sin x))

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)AA x,y in R and if f(2)=5, then find the value of f(f(2))

Let f(x+(1)/(y))+f(x-(1)/(y))=2f(x)f((1)/(y))AA x,y in R,y!=0 and f(0)=0 then the value of f(1)+f(2)=

If f(2(x)/(y))=f(2x)-f(y) for all x,y>0 and f(3)=2, then the value of [f(7)], is

If f((x+2y)/(3))=(f(x)+2f(y))/(3)AA x,y in R and f'(0)=1,f(0)=2 then find f(x) .

Suppose that fis differentiable function with the proporty f(x+y)=f(x)+f(y)+x^(2)y and lim_(x rarr0)(f(x))/(x)=0 ,then find the value of f'(10)

If f:R-{-1}rarr R and f is differentiable function satisfies f(x+f(y)+xf(y))=y+f(x)+y.f(x) for all x,y belongs to R-{-1} then find the value of 2010[1+f(2009)]