Question 57
Prove that there is no injective function $f: \mathbb{R} \to \mathbb{R}$ such that
$$
f(f(x) + y) = f(x + y) + f(2012) \quad \text{for all } x, y \in \mathbb{R}.
$$
$$
f(f(x) + y) = f(x + y) + f(2012) \quad \text{for all } x, y \in \mathbb{R}.
$$