Variation 1 · answer guide

Inverse function — Fixed point slopes

Question

If and intersect at on and , the slope of at that point 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..
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: Inverse-function derivative formula at a fixed point.

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