The domain of sqrt(x) is which of the following?

• A. x ≥ 0
• B. x ≤ 0
• C. All real numbers
• D. 0 ≤ x ≤ 1

Answer: (A)

The main idea is that the square root of a real number is defined only when the inside value is nonnegative. So for sqrt(x) to be a real number, x must be at least zero. That means the domain includes all nonnegative real numbers, often written as x ≥ 0 or [0, ∞). If x were negative, sqrt(x) wouldn’t be a real number, so those values aren’t allowed. The option that captures all nonnegative numbers is the correct domain. The other possibilities either include negative x (which aren’t allowed) or restrict x to a narrower range than the nonnegative set, missing valid inputs like x = 4.