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9231 P11 - Nov 2023 - Q07
4184

The curve C has equation \(y = f(x)\), where \(f(x) = \frac{x^2 + 2}{x^2 - x - 2}\).

  1. Find the equations of the asymptotes of C.
  2. Find the coordinates of any stationary points on C, giving your answers correct to 1 decimal place.
  3. Sketch C, stating the coordinates of any intersections with the axes.
  4. Sketch the curve with equation \(y = \frac{1}{f(x)}\).
  5. Find the set of values for which \(\frac{1}{f(x)} < f(x)\).
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