If U = R and A = {x ∈ R : x² − 9 > 0}, what is A′?
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Answer and explanation
Correct answer: [-3,3]
Factor the inequality as x² − 9 = (x−3)(x+3). The product is positive when x < −3 or x > 3, so A = (−∞,−3) ∪ (3,∞). The points −3 and 3 make the expression zero and are not in A. Consequently, the complement in R contains every number from −3 through 3, including both endpoints: A′ = [−3,3].
Frequently asked questions
What is the correct answer to this question?
[-3,3]
Why is this the correct answer?
Factor the inequality as x² − 9 = (x−3)(x+3). The product is positive when x < −3 or x > 3, so A = (−∞,−3) ∪ (3,∞). The points −3 and 3 make the expression zero and are not in A. Consequently, the complement in R contains every number from −3 through 3, including both endpoints: A′ = [−3,3].
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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