What is the domain of the function f(x) = log₁₀(x² - 5x + 6)?

Model Answer & Options

Source: Extra Practice

(2, 3)

(-∞, 2) ∪ (3, ∞)

(-∞, 2] ∪ [3, ∞)

R - {2, 3}

Explanation

For log(g(x)) to be defined, g(x) must be greater than zero. So, x² - 5x + 6 > 0. Factoring the quadratic gives (x - 2)(x - 3) > 0. Using the wavy curve method or testing intervals: the expression is positive when x 3. Thus, the domain is (-∞, 2) ∪ (3, ∞). Option A is wrong because it's the interval where the quadratic is negative.

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