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What is (f+g)(x)(f + g)(x)?\newlinef(x)=x2+3xf(x) = x^2 + 3x\newlineg(x)=−3x2g(x) = -3x^2\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)=x2+3xf(x) = x^2 + 3x\newlineg(x)=−3x2g(x) = -3x^2\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). \newline(f+g)(x)(f + g)(x) is the sum of f(x)f(x) and g(x)g(x). \newline(f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x)
  2. Add functions: We have: \newlinef(x)=x2+3xf(x) = x^2 + 3x \newlineg(x)=−3x2g(x) = -3x^2 \newlineNow, we will add f(x)f(x) and g(x)g(x) to find (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)=(x2+3x)+(−3x2)(f + g)(x) = (x^2 + 3x) + (-3x^2)
  3. Combine like terms: Combine like terms to simplify the expression. \newline(f+g)(x)=x2+3x−3x2(f + g)(x) = x^2 + 3x - 3x^2\newline(f+g)(x)=−2x2+3x(f + g)(x) = -2x^2 + 3x

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