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Home » The shaded region is the area of the square minus the area of the circle: - inBeat

The shaded region is the area of the square minus the area of the circle: - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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Observe that the right-hand side is a perfect cube:
Question: A postdoctoral researcher defines a function $ f $ recursive...
and $ f(1) = 3 $. We aim to find $ f(2025) $.
Since $ f(1) = 3 $, this gives $ f(3) = 5 $.
Now apply the equation at $ x = 3 $:
f(f(x)) = f(x + 2) = (x + 2) + 2 = x + 4,
2f(x) - x = 2(x + 2) - x = 2x + 4 - x = x + 4.
So $ f(f(x)) = 2f(x) - x $ holds. Also, $ f(1) = 3 $, which matches.
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