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MathNet 2021 — Part 01 Question 91

Math Olympiad Vault · MathNet 2021 — Part 01

Question 91

Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
f(x^2 + y) \ge \left(\frac{1}{x} + 1\right) f(y)
$$
holds for all $x \in \mathbb{R} \setminus \{0\}$ and all $y \in \mathbb{R}$.