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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−2x2+9xf(x) = -2x^2 + 9x\newlineg(x)=−x2g(x) = -x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=−2x2+9xf(x) = -2x^2 + 9x\newlineg(x)=−x2g(x) = -x^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).(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. Add functions: We have: \newlinef(x)=−2x2+9xf(x) = -2x^2 + 9x \newlineg(x)=−x2g(x) = -x^2\newlineNow, we need to add these two functions 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)=(−2x2+9x)+(−x2)(f + g)(x) = (-2x^2 + 9x) + (-x^2)
  3. Combine like terms: Combine the like terms to simplify the expression.\newline(f+g)(x)=−2x2+9x−x2(f + g)(x) = -2x^2 + 9x - x^2\newline(f+g)(x)=−3x2+9x(f + g)(x) = -3x^2 + 9x

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