If `f((xy)/(2)) = (f(x).f(y))/(2), x, y in R, f(1) = f'(1)."Then", (f(3))/(f'(3))`is.........

Let f((x+y)/(2))=(f(x)+f(y))/(2),x,y in R, if f'(0)=-1, then f'((x)/(2))=

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) .

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).

If f(x)f(y) + 2 = f(x) + f(y) + f(xy) and f(1) = 2, f'(1) = 2, then find f(x).

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

Let f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

If f' ((x)/(y)). f((y)/(x))=(x^(2)+y^(2))/(xy) AA x,y in R^(+) and f(1)=1 , then f^(2) (x) is

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