If f(x) = √(x + 1) and g(x) = √(x − 3), what is the domain of (f − g)(x)?

Correct answer: [3, ∞)

The governing concept is that the domain of a sum or difference of functions is the intersection of the domains of both component functions. For f(x) = √(x + 1), the radicand must be nonnegative: x + 1 ≥ 0, so x ≥ −1. For g(x) = √(x − 3), we need x − 3 ≥ 0, so x ≥ 3. Both conditions must hold simultaneously; therefore the common domain is [−1, ∞) ∩ [3, ∞) = [3, ∞). The endpoint 3 is included because √0 is defined, so excluding it would be incorrect. Hence option A is correct. Option B ignores g’s restriction, option C incorrectly gives an upper endpoint, and option D excludes a valid endpoint.