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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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Best 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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