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📅 May 1, 2026 👤 scraface

May 01, 2026

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Find the inverse of the function \( f(x) = rac{2x + 3}{x - 1} \).
Set \( y = rac{2x + 3}{x - 1} \).
Swap \( x \) and \( y \): \( x = rac{2y + 3}{y - 1} \).
Cross-multiply: \( x(y - 1) = 2y + 3 \).
Expand: \( xy - x = 2y + 3 \).
Rearrange: \( xy - 2y = x + 3 \).
Factor: \( y(x - 2) = x + 3 \).
Solve for \( y \): \( y = rac{x + 3}{x - 2} \).
#### Inverse: \( f^{-1}(x) = rac{x + 3}{x - 2} \)
Evaluate the limit \( \lim_{x o 2} rac{x^2 - 4}{x - 2} \).

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