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MathNet 2021 — Part 06 Question 43

Math Olympiad Vault · MathNet 2021 — Part 06

Question 43

Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that for all real numbers $x$ and $y$
$$
f(y - f(x)) = f(x) - 2x + f(f(y)).
$$