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Home » Topsters 3: The Revolutionary Tool That’s Taking the World by Storm! - Baxtercollege

Topsters 3: The Revolutionary Tool That’s Taking the World by Storm! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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f(a + b + c) = f(a) + f(b) + f(c)
and
f(ab) = f(a)f(b)
Solution: We are given two functional equations:
$ f(a + b + c) = f(a) + f(b) + f(c) $ for all real $ a, b, c $
$ f(ab) = f(a)f(b) $ for all real $ a, b $
We aim to find all such functions $ f : \mathbb{R} \to \mathbb{R} $.
Let’s try constant functions first. Suppose $ f(x) = c $ for all $ x $...
$ f(a + b + c) = c $, and $ f(a) + f(b) + f(c) = c + c + c = 3c $, so...
Also, $ f(ab) = 0 = 0 \cdot 0 = f(a)f(b) $, so the zero function works...

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