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← 2024 HSC Extension 1 paper Question 5

Variation 2 · answer guide

Inverse trigonometric functions — Outer and inner both

Question

Transformations taking to are

  1. vertical factor , horizontal factor
  2. vertical factor , horizontal factor
  3. vertical factor , horizontal factor
  4. vertical factor , horizontal factor

This practice question was inspired by Question 5 in the 2024 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: use the restricted domain and range that make the inverse function single-valued.Factor outside: vertical dilation by .
  2. Finish the calculation, then check that the result meets the question’s conditions.Argument : horizontal dilation by .
  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: Domain becomes ; range becomes .

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

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