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

Correct answer: ([0,\infty))

The sum \((f+g)(x)\) is defined only where both \(f(x)\) and \(g(x)\) are defined. The function \(f(x)=\sqrt{x}\) requires the quantity inside the square root to be nonnegative, so \(x\ge0\). The function \(g(x)=x+2\) is defined for every real number. Their common domain is therefore \([0,\infty)\), making option A correct.

Indeed, \((f+g)(x)=\sqrt{x}+x+2\). For \(x=0\) and positive values, the square root is real. For a negative value such as \(x=-1\), \(\sqrt{-1}\) is not real in the usual real-number setting, so the sum is not defined. The linear function does not add any further restriction.