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Home » Dark Wallpaper Hacks You’ve Been Searching For—Shock Your Screen NOW! - Imagemakers

Dark Wallpaper Hacks You’ve Been Searching For—Shock Your Screen NOW! - Imagemakers

📅 May 2, 2026 👤 scraface

May 02, 2026

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Question: For all real numbers $ a, b, c $, find the number of functio...
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...

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