Variation 3 · answer guide

Inverse trigonometric functions — Identity interval

Question

On which largest closed interval about is for all in the interval?

This practice question was inspired by Question 9 in the 2021 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.This is exactly the range of , on which is the identity.
Finish the calculation, then check that the result meets the question’s conditions.Outside it, e.g. at , .
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: Check endpoints: .

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