Determine the domain of g(x) = sqrt(x - 2).

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Multiple Choice

Determine the domain of g(x) = sqrt(x - 2).

Explanation:
A square root requires a nonnegative input. For g(x) = sqrt(x - 2), the inside must satisfy x - 2 ≥ 0. Solving gives x ≥ 2. So the domain includes all real numbers from 2 up to infinity, written as [2, ∞). It includes x = 2 because sqrt(0) = 0. Values less than 2 make the radicand negative, which isn’t allowed for real-valued square roots.

A square root requires a nonnegative input. For g(x) = sqrt(x - 2), the inside must satisfy x - 2 ≥ 0. Solving gives x ≥ 2. So the domain includes all real numbers from 2 up to infinity, written as [2, ∞). It includes x = 2 because sqrt(0) = 0. Values less than 2 make the radicand negative, which isn’t allowed for real-valued square roots.

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