If A = {x ∈ ℝ : x² < 9}, what is the interval form of A?
Answer and explanation
Correct answer: (-3, 3)
The governing idea is that x² < 9 means |x| < 3, because x² measures the square of the distance of x from zero. Thus −3 < x < 3. The inequality is strict, so the endpoint values −3 and 3 are excluded; interval notation therefore uses parentheses. Option A, (−3, 3), is correct. Option B wrongly includes the endpoints, while C describes values outside the interval and D confuses x with x².
Frequently asked questions
What is the correct answer to this question?
(-3, 3)
Why is this the correct answer?
The governing idea is that x² < 9 means |x| < 3, because x² measures the square of the distance of x from zero. Thus −3 < x < 3. The inequality is strict, so the endpoint values −3 and 3 are excluded; interval notation therefore uses parentheses. Option A, (−3, 3), is correct. Option B wrongly includes the endpoints, while C describes values outside the interval and D confuses x with x².
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
