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Home » \(d = ut + \frac12at^2\) - IX Labs

\(d = ut + \frac12at^2\) - IX Labs

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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)}

📌 Now plug in $ a = 1, b = 0 $:

📌 f(1) + f(1) = 2f(1) + 2f(0) \Rightarrow 2 = 2 + 2f(0) \Rightarrow f(0) = 0

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