What is the domain of f(x) = √(x − 7) + 2?

Correct answer: [7, ∞)

The governing concept is the real-existence condition for a square root: its radicand must be non-negative. In this function the radicand is x − 7, so we require x − 7 ≥ 0. Adding 7 to both sides gives x ≥ 7. Thus every real number from 7 onward is allowed, including 7 itself because √0 is defined. The added constant +2 is outside the radical; it changes output values but does not impose any new restriction on x. Therefore the domain is [7, ∞), making option A correct. Option B confuses the outside constant with the input restriction, option C reverses the inequality, and option D incorrectly includes values less than 7.