Variation 1 · answer guide

Inverse function — Horizontal line preimages

Question

How many real solutions does have?

This practice question was inspired by Question 9 in the 2023 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. or .
Finish the calculation, then check that the result meets the question’s conditions. (two solutions) and (two solutions): four real roots.
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: Both branches give positive squares.

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