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"Highlight Your Brown Hair Like a Pro: The Ultimate Looks You Need to Try NOW! - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Thus, the leading coefficient of $ f(x) $ is $ \boxed{3} $.

📌 Question: A function $ f: \mathbb{R} \to \mathbb{R} $ satisfies $ f(a + b) + f(a - b) = 2f(a) + 2f(b) $ for all real $ a, b $. If $ f(1) = 1 $, find $ f(2) $.

📌 Solution: Let’s plug in $ a = b = 1 $ into the functional equation:

📌 f(2) + f(0) = 2f(1) + 2f(1) = 4

📌 We are given $ f(1) = 1 $, so:

📌 f(2) + f(0) = 4 \quad \text{(1)}

📌 Now plug in $ a = 0, b = 1 $:

📌 f(1) + f(-1) = 2f(0) + 2f(1) \Rightarrow 1 + f(-1) = 2f(0) + 2 \Rightarrow f(-1) = 2f(0) + 1 \quad \text{(2)}

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