Inverse function — An inverse cubic

Question

Find the inverse of .

This practice question was inspired by Question 10 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.

Set up the solution: replace the function value by y, swap x and y, then solve for y..
Simplify the previous line carefully, keeping exact values where possible..
Finish the calculation, then check that the result meets the question’s conditions.Swap variables to obtain .
Match the result to the choices and state the correct option.Therefore option B is correct:

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.