Evaluating a reciprocal functional equation

Proved

WorkbookSource.problem_9739

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

lean-workbooksource-checked

If f is a function such that $f(x)+\frac{1}{x}\left[f\left(-\frac{1}{x}\right)\right]=3$ , what is the value of $f(2)$ ? Express your answer as a common fraction.

Source: InternLM Lean-Workbook, record lean_workbook_9739 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_9739 (f : ℝ → ℝ) (hf : ∀ x, f x + 1/x * f (-1/x) = 3) : f 2 = 3/4  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_9739; Apache-2.0

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