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where to watch dune 2 - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Also, $ f(ab) = 0 = 0 \cdot 0 = f(a)f(b) $, so the zero function works.

📌 Now suppose $ f $ is not constant.

📌 Let’s try additive functions satisfying both properties. From the additive condition, set $ c = 0 $:

📌 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 $

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