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← 2020 HSC Extension 1 paper Question 2

Variation 3 · answer guide

Inverse function — Negative vertical shift

Question

Given , what are the domain and range of ?

  1. ,\
  2. ,\
  3. ,\
  4. ,\

This practice question was inspired by Question 2 in the 2020 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.Domain of : . Range of : .
  2. Finish the calculation, then check that the result meets the question’s conditions.Swap: domain of is , range is .
  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: and .

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

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