Question 103
Find all non-decreasing and all non-increasing functions $f : [0; +\infty) \to \mathbf{R}$ such that for all $x, y \ge 0$ the equality
$$
f(x+y) - f(x) - f(y) = f(xy+1) - f(xy) - f(1)
$$
holds, and additionally $f(3) + 3f(1) = 3f(2) + f(0)$.
$$
f(x+y) - f(x) - f(y) = f(xy+1) - f(xy) - f(1)
$$
holds, and additionally $f(3) + 3f(1) = 3f(2) + f(0)$.