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

A function f : R -> R^+ satisfies f(x+y)= f(x) f(y) AA x in R If f'(0)=2 then 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 )/( 2)) = (f (x) + f (y))/( 2) AA x,y,in R. If f (0) =1. f '(0) exists and equal -1, find f' (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) .

Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k , then

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

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: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 + 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 : R to R is continuous such that f(x + y) = f(x) + f(y) x in R , y in R and f(1) = 2 then f(100) =