The function is defined by for . Find the rule and domain of the inverse function .
Answer and explanation
Correct answer: A. with domain
- Step 1: Express . Since , , so the range of is , which becomes the domain of .
- 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 .
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