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Home » The Ultimate Guide to Where to Stay in Rome—Live Like a Local Today! - Baxtercollege

The Ultimate Guide to Where to Stay in Rome—Live Like a Local Today! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 This is a well-known equation. Set $ x = 0 $:

📌 f(y) + f(-y) = 2f(0) + 2f(y) \Rightarrow f(-y) = 2f(0) + f(y).

📌 Now set $ y = 0 $:

📌 f(x) + f(x) = 2f(x) + 2f(0) \Rightarrow 2f(x) = 2f(x) + 2f(0) \Rightarrow f(0) = 0.

📌 So $ f(-y) = f(y) $, hence $ f $ is even.

📌 Now, the equation becomes:

📌 f(x + y) + f(x - y) = 2f(x) + 2f(y).

📌 Take $ x = y $:

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