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2020 HSC Mathematics Extension 1

Question 2:
Inverse function

1 markinverse functions

Given , what are the domain and range of ?

  1. ,\
  2. ,\
  3. ,\
  4. ,\

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

  1. For : domain and range (because ).
  2. The inverse swaps domain and range: domain of equals range of , and range of equals domain of .
  3. Hence domain of is and range of is .
  4. Explicit check: with ; after swapping, for , outputting values .
  5. Answer: C.

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

Given , what are the domain and range of ?

  1. ,\
  2. ,\
  3. ,\
  4. ,\
See the step-by-step answer guide →

Question 2

Given , what are the domain and range of ?

  1. ,\
  2. ,\
  3. ,\
  4. ,\
See the step-by-step answer guide →

Question 3

Given , what are the domain and range of ?

  1. ,\
  2. ,\
  3. ,\
  4. ,\
See the step-by-step answer guide →