The function is defined by for . Find the rule and domain of the inverse function .

Answer and explanation

Correct answer: A. with domain

  1. Step 1: Express . Since , , so the range of is , which becomes the domain of .
  2. Step 2: Rearrange the relation to express in terms of : . Swapping variables yields with domain .
Answer
with domain .
Why not the others: The option with domain mistakenly reuses the domain of instead of its range; the rule makes sign errors when moving terms across the equals sign; the domain ignores the restricted domain .

Practise more Functions, Graphing Techniques and Transformations.

Free questions with an explanation for every one, and full timed Singapore GCE A-Level mock tests.