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Home » Let the width be \( w \) meters. Then, the length is \( w + 4 \) meters. - Deep Underground Poetry

Let the width be \( w \) meters. Then, the length is \( w + 4 \) meters. - Deep Underground Poetry

📅 May 6, 2026 👤 scraface

May 06, 2026

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\boxed{\langle 1, t, 1 \rangle \text{ for any } t \in \mathbb{R}}
Find the range of the function \( f(x) = \frac{x^2 + 1}{x^2 - 1} \) as...
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.
Analyzing the sign of the expression:

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