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What is (f+g)(x)(f + g)(x)?\newlinef(x)=2x2+7xf(x) = 2x^2 + 7x\newlineg(x)=−3xg(x) = -3x\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)=2x2+7xf(x) = 2x^2 + 7x\newlineg(x)=−3xg(x) = -3x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify formula: Identify the formula for (f+g)(x)(f + g)(x).(f+g)(x)(f + g)(x) is the sum of f(x)f(x) and g(x)g(x).(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)
  2. Calculate sum: We have:\newlinef(x)=2x2+7xf(x) = 2x^2 + 7x\newlineg(x)=−3xg(x) = -3x\newlineNow, let's find (f+g)(x)(f + g)(x) by adding f(x)f(x) and g(x)g(x) together.\newline(f+g)(x)=(2x2+7x)+(−3x)(f + g)(x) = (2x^2 + 7x) + (-3x)
  3. Combine like terms: Combine like terms.\newline(f+g)(x)=2x2+7x−3x(f + g)(x) = 2x^2 + 7x - 3x\newline(f+g)(x)=2x2+(7x−3x)(f + g)(x) = 2x^2 + (7x - 3x)\newline(f+g)(x)=2x2+4x(f + g)(x) = 2x^2 + 4x

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