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Home » Milquetoast Meaning Explained: The Crystal-Clear Truth Behind the Word! - ECD Germany

Milquetoast Meaning Explained: The Crystal-Clear Truth Behind the Word! - ECD Germany

📅 May 10, 2026 👤 scraface

May 10, 2026

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📌 Find the range of the function \( f(x) = \frac{x^2 + 1}{x^2 - 1} \) as \( x \) ranges over all real numbers such that \( x \neq \pm 1 \).

📌 Let \( y = \frac{x^2 + 1}{x^2 - 1} \). Rearranging gives:

📌 y(x^2 - 1) = x^2 + 1 \quad \Rightarrow \quad yx^2 - y = x^2 + 1.

📌 Rearranging terms:

📌 If \( y \neq 1 \),

📌 x^2 = \frac{y + 1}{y - 1}.

📌 Since \( x^2 \geq 0 \), we require:

📌 \frac{y + 1}{y - 1} \geq 0.

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