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The domain of the function f : R → R defined by \(f(x)=\sqrt{x^2 - 3x + 2}\) is:1. (-∞, 1] ∪ [2, ∞) 2. (-∞, 1) ∪ (2, ∞)3. (-∞, -3) ∪ (3, ∞)4. (-∞, -3] ∪ [3, ∞) |
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Answer» Correct Answer - Option 1 : (-∞, 1] ∪ [2, ∞) Concept: We know that the domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes. Given: \(f\left( x \right) = \sqrt {{x^2} - 3x + 2} \) Analysis: For domain, f(x) ≥ 0 \(\sqrt {{x^2} - 3x + 2} \ge 0\) (x - 2) (x - 1) ≥ 0 Case: 1 (x - 2) ≥ 0 and (x – 1) ≥ 0 x ≥ 2 and x ≥ 1 overall: x ≥ 2 {x|2 ≤ x < ∞} = [2, ∞) Case: 2 (x - 2) ≤ 0 and (x - 1) ≤ 0 x ≤ 2 and x ≤ 1 overall : x ≤ 1 {x|-∞ < x ≤ 1} = (-∞, 1] ∴ The domain of the function is: (-∞, 1] ∪ [2, ∞) |
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