If A = {x ∈ ℝ : x² ≤ 16}, which interval represents A?
Answer and explanation
Correct answer: [-4, 4]
The relevant principle is |x| ≤ 4, since taking the nonnegative square root of x² ≤ 16 gives a distance from zero no greater than 4. Equivalently, −4 ≤ x ≤ 4. Equality is allowed, so both boundary points −4 and 4 belong to the set and square brackets are required. Therefore option B, [−4, 4], is correct. Option A excludes valid endpoints, C represents the outside region, and D lists squared values rather than possible x-values.
Frequently asked questions
What is the correct answer to this question?
[-4, 4]
Why is this the correct answer?
The relevant principle is |x| ≤ 4, since taking the nonnegative square root of x² ≤ 16 gives a distance from zero no greater than 4. Equivalently, −4 ≤ x ≤ 4. Equality is allowed, so both boundary points −4 and 4 belong to the set and square brackets are required. Therefore option B, [−4, 4], is correct. Option A excludes valid endpoints, C represents the outside region, and D lists squared values rather than possible x-values.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
