What is the domain of the function f(x) = √[(x - 4) / (x - 6)]?

Model Answer & Options

Source: Extra Practice

[4, 6]

(-∞, 4] ∪ (6, ∞)

(-∞, 4) ∪ [6, ∞)

[4, 6)

Explanation

For the square root to be defined, the expression inside must be ≥ 0: (x - 4) / (x - 6) ≥ 0. Critical points are 4 and 6. The denominator cannot be zero, so x ≠ 6. Testing intervals: for x ≤ 4, e.g., 0, (-4)/(-6) = 2/3 ≥ 0 (True). For 4 < x < 6, e.g., 5, (1)/(-1) = -1 6, e.g., 7, (3)/(1) = 3 ≥ 0 (True). Thus, the domain is (-∞, 4] ∪ (6, ∞).

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