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)=(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) = 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

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

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

If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to

If f((x)/(y))=(f(x))/(f(y)) forall x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4 . Then, f(5) is

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

Let f: R rarr R be a differentiable function satisfying f(x+y)=f(x)+f(y)+x^(2)y+xy^(2) for all real numbers x and y. If lim_(xrarr0) (f(x))/(x)=1, then The value of f(9) is

Let f((x+y)/(2))=(f(x)+f(y))/(2) and f(0)=b. Find f''(x) (where y is independent of x), when f(x) is differentiable.

If 2f(x)=f(x y)+f(x/y) for all positive values of x and y,f(1)=0 and f'(1)=1, then f(e) is.