Question 2
Find all nondecreasing functions $ f\colon \mathbb{R} \longrightarrow \mathbb{R} $ such that
(i) $ f(0)=0, f(1)=1; $
(ii) $ f(a) + f(b) = f(a)f(b) + f(a + b - ab) $ for all real numbers a, b such that a < 1 < b.
(i) $ f(0)=0, f(1)=1; $
(ii) $ f(a) + f(b) = f(a)f(b) + f(a + b - ab) $ for all real numbers a, b such that a < 1 < b.