What is the domain of the function f(x) = sqrt(3x - 6)?

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Multiple Choice

What is the domain of the function f(x) = sqrt(3x - 6)?

Explanation:
The domain of a square root function is determined by requiring the expression inside the root to be nonnegative. For f(x) = sqrt(3x - 6), you need 3x - 6 ≥ 0. Solving gives 3x ≥ 6, so x ≥ 2. This means every x that is at least 2 makes the radicand nonnegative, including x = 2 where f(2) = 0. Values less than 2 would make 3x - 6 negative, which isn’t allowed for real-valued outputs. Thus the domain is all real numbers x with x ≥ 2.

The domain of a square root function is determined by requiring the expression inside the root to be nonnegative. For f(x) = sqrt(3x - 6), you need 3x - 6 ≥ 0. Solving gives 3x ≥ 6, so x ≥ 2. This means every x that is at least 2 makes the radicand nonnegative, including x = 2 where f(2) = 0. Values less than 2 would make 3x - 6 negative, which isn’t allowed for real-valued outputs. Thus the domain is all real numbers x with x ≥ 2.

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