What is the domain of f(x) = sqrt(x)?

• A. x < 0
• B. All real numbers
• C. x ≥ 0
• D. x > 0

Answer: (C)

The domain of a real-valued square root function is all x values that make the radicand nonnegative, because you can’t take the real square root of a negative number. That means x must be greater than or equal to zero. So the domain is x ≥ 0 (all nonnegative numbers). At x = 0, you get sqrt(0) = 0, and for larger x you get positive outputs. If you stayed in the real numbers, negative x aren’t allowed because they would produce imaginary results; in contexts allowing complex numbers, the domain would be treated differently.