Source: Extra Practice
What is the domain of the function f(x) = log₁₀(x² - 5x + 6)?
Options
Option A
(2, 3)
Option B is correct
(-∞, 2) ∪ (3, ∞)
Option C
(-∞, 2] ∪ [3, ∞)
Option D
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.