Question 155
Let $P(x) \in \mathbb{R}[x]$ be a monic, non-constant polynomial. Determine all continuous functions $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(f(P(x)) + y + 2023f(y)) = P(x) + 2024f(y),
$$
for all reals $x, y$.
$$
f(f(P(x)) + y + 2023f(y)) = P(x) + 2024f(y),
$$
for all reals $x, y$.