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Home » 10 Odd Facts About Mexico No Tourist Guides Reveal—Brace Yourself! - Dyverse

10 Odd Facts About Mexico No Tourist Guides Reveal—Brace Yourself! - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 f(a + b) = f(a) + f(b)

📌 So $ f $ is additive. Also, from the multiplicative condition:

📌 So $ f $ is both additive and multiplicative. These are very restrictive properties.

📌 Known result: The only functions $ f : \mathbb{R} \to \mathbb{R} $ that are both additive and multiplicative are:

📌 $ f(x) = 0 $ for all $ x $

📌 $ f(x) = x $ for all $ x $

📌 Let’s verify both:

📌 $ f(x) = 0 $: $ f(a + b + c) = 0 = 0 + 0 + 0 = f(a) + f(b) + f(c) $, and $ f(ab) = 0 = 0 \cdot 0 = f(a)f(b) $ — OK

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