doubt

[Kajol]

Suppose f(x,y) where x and y are real, is a differentiable function satisfying the following properties:

1) f(x+k,y) = f(x,y) + ky;

2) f(x, y+k) = f(x,y) + kx;

3) f(x,0) = m, where m is a constant

Then f(x,y) is given by

(A) m + xy

(B) m+x+y

(C) mxy

(D) none of the above

[samuraijack]

Answer a)
solve it from options