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-1and 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)-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) = 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

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+y)=f(x)+f(y)+c, for all real x and y and f(x) is continuous at x=0 and f'(0)=-1 then f(x) equals to

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

"Let" f(x+y)=f(x)f(y) "for all x,y, where" f(0)ne0 . If f'(0)=2, then f(x) is equal to