`f((x+y)/2)=(f(x)+f(y))/2 AA x,y in R and f(0) = 1 and f'(0) = -1` and function is differentiable for all x, then find `f(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

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

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AA x,y in R and f(0)!=0 ,then f(x) is an even function f(x) is an odd function If f(2)=a, then f(-2)=a If f(4)=b, then f(-4)=-b

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

A function f : R to R satisfies the equation f(x + y) = f(x), f(y) for all x, y in R , f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f' (0) = 2. Find (f'(x))/f(x)

If f(x) is a function satisfies the relation for all x,y in R,f(x+y)=f(x)+f(y) and if f'(0)=2 andfunction is differentiable every where,then find f(x)