Question 8
Find all functions $f : \mathbb{R} \to \mathbb{R}$ satisfying the conditions:
(i) $f(f(x^2) + y + f(y)) = x^2 + 2f(y)$;
(ii) $x \le y$ implies $f(x) \le f(y)$;
for all real numbers $x$ and $y$.
(i) $f(f(x^2) + y + f(y)) = x^2 + 2f(y)$;
(ii) $x \le y$ implies $f(x) \le f(y)$;
for all real numbers $x$ and $y$.