If f(x)=√(x+4) and g(x)=1/(x-1), what is the domain of (f+g)(x)?

Correct answer: [-4,∞)\{1}

The governing concept is that the domain of a sum is the intersection of the domains of its component functions. For f(x)=√(x+4), the radicand must be nonnegative: x+4≥0, so x≥-4. For g(x)=1/(x-1), the denominator cannot vanish, so x≠1. Combining both restrictions gives [-4,∞) with the single point 1 removed. The endpoint -4 is included because the square root of zero is defined. Option B forgets the denominator restriction, option C allows values less than -4 where the square root is not real, and option D removes too much of the valid interval. Hence option A is correct.