If \(f(x)=\frac{1}{1+\sqrt{x}}\), what are its domain and range, respectively?

Correct answer: \(\big([0,\infty),(0,1]\big)\)

The square root requires \(x\ge 0\), so the domain is \([0,\infty)\). At \(x=0\), \(f(0)=1\), so 1 is included in the range. As \(x\to\infty\), \(f(x)\to 0\), but the function never actually equals 0 for any finite \(x\). Hence the range is \((0,1]\). Exam tip: first impose the input restrictions, then check endpoint values and limiting values to determine the range.