Domain of f(x) = sqrt(x - 4)

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Multiple Choice

Domain of f(x) = sqrt(x - 4)

Explanation:
When you see a square root, the expression inside must be nonnegative to stay real. For f(x) = sqrt(x - 4), the inside is x - 4, so you need x - 4 ≥ 0. That leads to x ≥ 4. If x = 4, you get sqrt(0) = 0; if x > 4, you get a positive result. For x < 4, the radicand would be negative, which isn’t allowed in real numbers. So the domain is all real numbers x with x at least 4, i.e., [4, ∞).

When you see a square root, the expression inside must be nonnegative to stay real. For f(x) = sqrt(x - 4), the inside is x - 4, so you need x - 4 ≥ 0. That leads to x ≥ 4. If x = 4, you get sqrt(0) = 0; if x > 4, you get a positive result. For x < 4, the radicand would be negative, which isn’t allowed in real numbers. So the domain is all real numbers x with x at least 4, i.e., [4, ∞).

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