Variation 1 · answer guide

Inverse trigonometric functions — Inner scale only

Question

Compared with , the graph of is obtained by a horizontal dilation of factor

This practice question was inspired by Question 5 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.Argument compresses horizontally by .
Finish the calculation, then check that the result meets the question’s conditions.No vertical scale is present.
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: Domain shrinks from to .

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