If `f(x+y)=f(x)+f(y),AAx ,\ y in R` then prove that `f(k x)=kf(x)for\ AAk ,\ x in Rdot`

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(xy)AAx,y in R then prove that f is a constane function.

Let f(x + y) = f(x) .f(y) AA x, y in R suppose that f(k) =3, k in R and f'(0) = 11 then find f'(k)

Let f(x + y) = f(x) .f(y) AA x, y in R suppose that f(k) =3, k in R and f'(0) = 11 then find f'(k)

If f(x)=5^x , then prove : f(x+y)=f(x).f(y)

f((x)/(y))=f(x)-f(y)AA x,y in R^(+) and f(1)=1, then show that f(x)=In x

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)AA x,y in R and f(0)=k, then

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) = (x-1)/(x+1) , then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy) .