Solving a reflected functional equation

Proved

WorkbookSource.problem_18736

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Find the closed-form solution $f(x)$ to the equation: $f(x) + 2f(2-x) = 2x(2-x)$

Source: InternLM Lean-Workbook, record lean_workbook_18736 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_18736 (f : ℝ → ℝ) (hf : ∀ x, f x + 2 * f (2 - x) = 2 * x * (2 - x)) : ∀ x, f x = 2 * x * (2 - x) / 3  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_18736; Apache-2.0

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