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Home » Stop Middle Back Strengthening Pain—Try These Expert Back Stretches Now! - Midis

Stop Middle Back Strengthening Pain—Try These Expert Back Stretches Now! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Let $ y = \cos x $, where $ y \in [-1, 1] $. The function becomes:

📌 f(y) = -y^2 + 2y + 1.

📌 This is a quadratic opening downward. Its maximum occurs at the vertex $ y = \frac{-b}{2a} = \frac{-2}{-2} = 1 $. Evaluating at $ y = 1 $:

📌 f(1) = -1 + 2 + 1 = 2.

📌 Evaluate at $ y = -1 $:

📌 f(-1) = -1 - 2 + 1 = -2.

📌 Thus, the range of $ f(x) $ is $[-2, 2]$.

📌 \boxed{[-2, 2]}

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