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← 2022 HSC Extension 1 paper Question 9

Variation 3 · answer guide

Inverse function — Parallel possible

Question

Can the tangents to and be parallel at an intersection on ?

  1. Yes, when , i.e.
  2. Never
  3. Only when
  4. Only when the functions are constant

This practice question was inspired by Question 9 in the 2022 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.Parallel means equal slopes: .
  2. Finish the calculation, then check that the result meets the question’s conditions.Both are possible for invertible differentiable functions (e.g. ).
  3. 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: This shows option C of the original is not always true.

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

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