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Home » $ k = 0 $: $ -15^\circ $ — invalid - Parker Core Knowledge

$ k = 0 $: $ -15^\circ $ — invalid - Parker Core Knowledge

📅 May 2, 2026 👤 scraface

May 02, 2026

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f(x + y) + f(x - y) = 2f(x) + 2f(y) \quad \text{for all } x, y \in \ma...
This is a well-known equation. Set $ x = 0 $:
f(y) + f(-y) = 2f(0) + 2f(y) \Rightarrow f(-y) = 2f(0) + f(y).
Now set $ y = 0 $:
f(x) + f(x) = 2f(x) + 2f(0) \Rightarrow 2f(x) = 2f(x) + 2f(0) \Rightar...
So $ f(-y) = f(y) $, hence $ f $ is even.
Now, the equation becomes:
f(x + y) + f(x - y) = 2f(x) + 2f(y).
Take $ x = y $:
f(2x) + f(0

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