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What is (f+g)(x)(f + g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=2x2+xg(x) = 2x^2 + x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=2x2+xg(x) = 2x^2 + x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Define Functions: We have:\newlinef(x)=4xf(x) = 4x\newlineg(x)=2x2+xg(x) = 2x^2 + x\newlineNow, we add the two functions together to get (f+g)(x)(f + g)(x).\newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)\newline(f+g)(x)=4x+(2x2+x)(f + g)(x) = 4x + (2x^2 + x)
  2. Add Functions: Next, we combine like terms. Since there are no like terms with 2x22x^2, we just bring it down. We then combine the terms with xx.
    (f+g)(x)=2x2+(4x+x)(f + g)(x) = 2x^2 + (4x + x)
    (f+g)(x)=2x2+5x(f + g)(x) = 2x^2 + 5x

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