What is the domain of (f(x)=\sqrt{x-2}+\frac{1}{\sqrt{x-5}})?

Correct answer: ( (5,\infty) )

The direct answer is B: (5,∞). A square root requires its radicand to be non-negative, while a denominator can never be zero. For √(x-2), we need x-2≥0, so x≥2. For 1/√(x-5), the expression under the root must be positive, not merely non-negative, because the root is in the denominator: x-5>0, so x>5. Both conditions must hold at once. The stronger condition x>5 already guarantees x≥2, so the domain is (5,∞). Option A, [2,∞), incorrectly includes values from 2 through 5, where the denominator is either undefined or zero. Option B is correct because every x greater than 5 makes both terms meaningful and keeps the denominator non-zero. Option C, [5,∞), incorrectly includes x=5; then √(x-5)=0 and division by zero is impossible. Option D, (2,5), fails because the denominator square root is not real there. Common mistake: for a square root in a denominator, use a strict inequality.