Evaluating a composition at opposite inputs

Proved

WorkbookSource.problem_7260

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

lean-workbooksource-checked

Let $f(x) = 3x^2-7$ and $g(f(4)) = 9$ . What is $g(f(-4))$ ?

Source: InternLM Lean-Workbook, record lean_workbook_7260 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_7260 (f g : ℝ → ℝ) (hf : ∀ x, f x = 3 * x ^ 2 - 7) (hg : g (f 4) = 9) : g (f (-4)) = 9  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_7260; Apache-2.0

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