Question 5
Determine all strictly increasing functions $f: \mathbb{R} \to \mathbb{R}$ that satisfies the conditions:
$$
\bullet \quad f(x^3 + y^2 + f(y)) = x^2 f(x) + y f(y) + y;
$$
$$ \bullet \quad \text{Equality } y^2 + f(y) = t \text{ has a solution for every } t \in \mathbb{R}. $$
$$
\bullet \quad f(x^3 + y^2 + f(y)) = x^2 f(x) + y f(y) + y;
$$
$$ \bullet \quad \text{Equality } y^2 + f(y) = t \text{ has a solution for every } t \in \mathbb{R}. $$