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← 2023 HSC Extension 1 paper Question 9

Variation 3 · answer guide

Inverse function — Inverse swaps coordinates

Question

If a graph meets the line at exactly five points, the inverse relation meets at

  1. exactly five points
  2. exactly two points
  3. no points
  4. infinitely many points

This practice question was inspired by Question 9 in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: replace the function value by y, swap x and y, then solve for y.Swapping sends horizontal level to vertical line with the same multiplicity.
  2. Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Inverse relation is reflection in .

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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