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

Correct answer: [1, ∞)

For a quotient of real-valued functions, both square roots must be real and the denominator must be nonzero. The numerator g(x)=√(x−1) is real when x−1≥0, so x≥1. The denominator f(x)=√(x+3) is real when x+3≥0, so x≥−3; additionally, f(x) cannot equal zero, which would exclude x=−3. Combining all conditions gives x≥1. For every x in [1,∞), x+3 is at least 4, so the denominator is automatically positive and never zero. Therefore the domain is [1,∞), option A. Option D forgets the numerator restriction, B uses an incorrect lower bound, and C subtracts a value that is already outside [1,∞).