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Find the domain of the function f(x)=1/√(x²−3x+2).

1. (-∞, 1)
2. (-∞, 1) ∪ (2, ∞)
3. (-∞, 1] ∪ [2, ∞)
4. (2, ∞)

Correct answer: (-∞, 1) ∪ (2, ∞)

Solution

The function is undefined where the expression under the square root is non-positive, which occurs at the roots of the quadratic equation x²−3x+2=0. The roots are x=1 and x=2, leading to the intervals where the function is defined: (-∞, 1) and (2, ∞).

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