Let `f((x+y)/2)=(f(x)+f(y))/2` for all real x and y. If f'(0) exists and equals-1 and f(0)=1, find f(2)

Let f((x+y)/(2))=(f(x)+f(y))/(2) for all real x and y If f'(0) exists and equals -1 and f(0)=1, then find f(2)

Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y . If f'(0) exits and equals -1 and f(0) =1 , then find f(2) .

Let f((x+y)/(2))=(1)/(2)[f(x)+f(y)] for all real x and y. If f'(0) exists and equals (-1),f(0)=1 , find f(2).

Let f((x+y)/2) = (f(x)+f(y))/2 for all real values of x and y. If f^(')(0) exists and equals -1 and f(0) =1, then f^(')(2) is equal to

Let f((x+y)/(2))=1/2 |f(x) +f(y)| for all real x and y, if f '(0) exists and equal to (-1), and f(0)=1 then f(2) is equal to-

Let (f(x+y)-f(x))/(2)=(f(y)-a)/(2)+xy for all real x and y. If f(x) is differentiable and f'(0) exists for all real permissible value of a and is equal to sqrt(5a-1)-a^(2). Then f(x) is positive for all real xf(x) is negative for all real xf(x)=0 has real roots Nothing can be said about the sign of f(x)

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) .

Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists and f'(0) = - sin alpha , then f{f'(0)} is