The domain of f(x) = sqrt(x - 1) is which of the following?

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Multiple Choice

The domain of f(x) = sqrt(x - 1) is which of the following?

Explanation:
Determining the domain requires ensuring the expression under the square root is nonnegative. For f(x) = sqrt(x − 1), the radicand is x − 1, so we need x − 1 ≥ 0, which gives x ≥ 1. At x = 1, f(1) = sqrt(0) = 0, which is defined. For x < 1, the radicand is negative, and the square root would not yield a real value. Therefore, the function is defined for all real numbers x with x at least 1. The other options either include values that make the radicand negative or exclude x = 1, which is valid.

Determining the domain requires ensuring the expression under the square root is nonnegative. For f(x) = sqrt(x − 1), the radicand is x − 1, so we need x − 1 ≥ 0, which gives x ≥ 1. At x = 1, f(1) = sqrt(0) = 0, which is defined. For x < 1, the radicand is negative, and the square root would not yield a real value. Therefore, the function is defined for all real numbers x with x at least 1. The other options either include values that make the radicand negative or exclude x = 1, which is valid.

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