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← 2025 HSC Extension 1 paper Question 11(a)

Variation 2 · answer guide

Inverse function — An inverse cubic

Question

Find the inverse of .

This practice question was inspired by Question 11(a) in the 2025 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..
  2. Simplify the previous line carefully, keeping exact values where possible..
  3. Finish the calculation, then check that the result meets the question’s conditions.Swap variables to obtain .
  4. State the final answer clearly in the form the question requested.Final answer:

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

Verification: Substitution into returns x.

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

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