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how to calculate the slope of a line - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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Thus, \(\mathbf{v} = \langle 1, t, 1 \rangle\) for any real \(t\).
\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.

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