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Home » read this article and answer the questions that follow - RTA

read this article and answer the questions that follow - RTA

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Question: For all real numbers $ a, b, c $, find the number of functions $ f : \mathbb{R} \to \mathbb{R} $ such that

📌 f(a + b + c) = f(a) + f(b) + f(c)

📌 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} $.

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