A value fixed by a functional equation

Proved

WorkbookSource.problem_32186

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

lean-workbooksource-checked

Given $f(0)=0, f(1)=1$ , and $f(x^2+\frac{1}{x})=f(x)^2+f(\frac{1}{x})$ for all $x eq 0$ , find $f(2)$

Source: InternLM Lean-Workbook, record lean_workbook_32186 (Apache-2.0). The complete source proposition and its explicit variable declarations are preserved.

Preamble

import Mathlib
open Real

Formal statement

theorem WorkbookSource.problem_32186 (f : ℝ → ℝ) (hf1 : f 0 = 0) (hf2 : f 1 = 1) (hf3 : ∀ x ≠ 0, f (x^2 + 1/x) = (f x)^2 + f (1/x)) : f 2 = 2  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_32186; Apache-2.0

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