What is the domain of f(x) = sqrt(x - 2)?

• A. x > 2
• B. x ≥ 0
• C. x ≥ 2
• D. x ≤ 2

Answer: (C)

When a function includes a square root, the expression inside the root must be nonnegative to produce real numbers. For f(x) = sqrt(x - 2), the radicand is x - 2, so require x - 2 ≥ 0. Solving gives x ≥ 2. That means the function is defined for all real x from 2 up to infinity, including 2 itself (since sqrt(0) = 0). Values less than 2 would make the inside negative, which isn’t allowed for real-valued square roots.