2025 HSC Mathematics Extension 1
Question 10:
Inverse function
For , it is known that , and . Let . What is ?
How to recognise this question
Question type: inverse functions
- The command and notation point to inverse functions.
- The requested response is a multiple choice.
How to handle it: replace the function value by y, swap x and y, then solve for y.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- For an inverse, .
- Differentiate the inverse relation again: .
- , so option C is correct.
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Find the inverse of .
Question 2
Find the inverse of .
Question 3
At , suppose , , . Find .