Find all nondecreasing functions
![f: \mathbb{R}\rightarrow\mathbb{R}](/media/m/1/6/b/16b5eb72b61b6f20d54e0d614060cc02.png)
such that
(i)
(ii)
![f(a) + f(b) = f(a)f(b) + f(a + b - ab)](/media/m/7/c/a/7ca2945cfe591dc9f1f7ee234414643c.png)
for all real numbers
![a, b](/media/m/a/2/b/a2bdbf048e2daac0a021a1d79f6fb9bf.png)
such that
![a < 1 < b](/media/m/b/2/8/b28cf2d8ce78c4613d482a1be25da32a.png)
.
%V0
Find all nondecreasing functions $f: \mathbb{R}\rightarrow\mathbb{R}$ 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 $a < 1 < b$.