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MathNet 2020 — Math Olympiad Vault — Part 02 Question 72

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 02

Question 72

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