Variation 2 · answer guide

Inverse function — Product of slopes on y=x

Question

At a fixed-point intersection with slope for , the product of the two tangent slopes is

This practice question was inspired by Question 9 in the 2022 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.Product .
Finish the calculation, then check that the result meets the question’s conditions.So the tangents are not perpendicular.
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: Reciprocal slopes multiply to 1.

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