If `f(x+y)=f(x)+f(y)` for all real x and y, show that `f(x)=xf(1)`.

If f(x+y) = f(x) * f(y) for all real x and y and f(5)=2,f'(0) = 3 , find f'(5).

The f(x) is such that f(x+y) = f(x) + f(y) , for all reals x and y xx then f(0) =

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

If f(x+y)=f(x)*f(y) for all real x,y and f(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^(2)) is an even function.

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is:

if f(x+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

If f (x) a polynomial function satisfying f (x) f (y) = f (x) + f(y) + f (xy) all real x and y and f(3) = 10, then f (4) – 8 is equal to