If \(f(x)=x^2+2\) and \(g(x)=2x\), which of the following is the completed-square form of \((f+g)(x)\)?

Correct answer: \((x+1)^2+1\)

For the sum of two functions, \((f+g)(x)=f(x)+g(x)=x^2+2+2x=x^2+2x+2\). Completing the square gives \(x^2+2x+2=(x^2+2x+1)+1=(x+1)^2+1\), so option A is correct. Option B would produce the term \(-2x\) instead of \(+2x\). Exam tip: for \(x^2+2x+a\), write it as \((x+1)^2+(a-1)\).