Variation 2 · answer guide

Inverse trigonometric functions — Scaled argument domain

Question

Domain of is

This practice question was inspired by Question 4 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.

Set up the solution: use the restricted domain and range that make the inverse function single-valued.Need , so .
Finish the calculation, then check that the result meets the question’s conditions.On that domain the expression equals constantly.
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: At the inverse trig functions are defined; outside they are not.

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