Which option is the correct roster form of G₁ = {x : x ∈ ℤ, x³ = x}?
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Answer and explanation
Correct answer: G₁ = {−1, 0, 1}
Rewrite the equation as x³ − x = 0 and factor it: x(x² − 1) = x(x − 1)(x + 1) = 0. Thus x can be 0, 1, or −1. All three values are integers, so all satisfy the stated domain. Substitution confirms that each gives x³ = x. Therefore, the roster form is option A.
Frequently asked questions
What is the correct answer to this question?
G₁ = {−1, 0, 1}
Why is this the correct answer?
Rewrite the equation as x³ − x = 0 and factor it: x(x² − 1) = x(x − 1)(x + 1) = 0. Thus x can be 0, 1, or −1. All three values are integers, so all satisfy the stated domain. Substitution confirms that each gives x³ = x. Therefore, the roster form is option A.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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