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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−2x+6f(x) = -2x + 6\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)=−2x+6f(x) = -2x + 6\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. Given functions: We have: \newlinef(x)=−2x+6f(x) = -2x + 6 \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)=(−2x+6)+(−x2)(f + g)(x) = (-2x + 6) + (-x^2)
  3. Combine functions: Combine like terms to simplify the expression.\newline(f+g)(x)=−x2−2x+6(f + g)(x) = -x^2 - 2x + 6\newlineThere are no like terms to combine further, so this is the simplest form.

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