If \(f(x)=\sqrt{x-2}\) and \(g(x)=\sqrt{10-2x}\), what is the domain of \((f+g)(x)\)?

Correct answer: \([2,5]\)

For a real square root, the expression inside the root must be non-negative. For \(f(x)\), \(x-2\ge 0\), so \(x\ge 2\). For \(g(x)\), \(10-2x\ge 0\), so \(x\le 5\). The sum \((f+g)(x)\) is defined only where both conditions hold; hence its domain is \([2,5]\). The closest distractor, \((2,5)\), is incorrect because square roots may equal zero at \(x=2\) and \(x=5\), so both endpoints are included. Exam tip: the domain of a sum is the intersection of the domains of the given functions.