If (f(x)=2x^2-3x+1) and (g(x)=x^2+x-5), what is ((f+g)(x))?

Correct answer: (3x^2-2x-4)

The correct answer is option A: \((f+g)(x)=3x^2-2x-4\). The symbol \(f+g\) means add the two function values: \((f+g)(x)=f(x)+g(x)\). Substitute the expressions: \((2x^2-3x+1)+(x^2+x-5)\). Combine like terms by degree: \(2x^2+x^2=3x^2\), \(-3x+x=-2x\), and \(1-5=-4\). Thus the result is \(3x^2-2x-4\). Option A matches every combined term. Option B changes the coefficient of \(x^2\) and the other terms, so it is not the sum. Option C incorrectly makes the linear coefficient positive, as if \(-3x+x=2x\). Option D leaves out one \(x^2\) contribution and has the wrong linear coefficient. Always add corresponding powers separately; do not multiply the functions or combine unlike terms. Memory cue: align the \(x^2\), x, and constant columns before adding.