Inverse function — Same g, different point setup

Question

With , note so . For , explain why is not the exam target, and compute as above.

This practice question was inspired by Question 14(e) 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: replace the function value by y, swap x and y, then solve for y.Exam asks at because is the convenient known inverse value.
State the final answer clearly in the form the question requested. as shown.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Gradient .

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