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What is (f+g)(x)(f + g)(x)?\newlinef(x)=x210xf(x) = -x^2 - 10x\newlineg(x)=xg(x) = -x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

Full solution

Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=x210xf(x) = -x^2 - 10x\newlineg(x)=xg(x) = -x\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). The correct formula is (f+g)(x)=f(x)+g(x)(f + g)(x) = f(x) + g(x).
  2. Substitute Values: We have f(x)=x210xf(x) = -x^2 - 10x and g(x)=xg(x) = -x. Substitute these values into the formula to get (f+g)(x)=(x210x)+(x)(f + g)(x) = (-x^2 - 10x) + (-x).
  3. Simplify Equation: Simplify the equation (f+g)(x)=(x210x)+(x)(f + g)(x) = (-x^2 - 10x) + (-x) to find (f+g)(x)(f + g)(x).\newline(f+g)(x)=x210xx(f + g)(x) = -x^2 - 10x - x
  4. Combine Like Terms: Combine like terms to get the final simplified form of (f+g)(x)(f + g)(x).(f+g)(x)=x211x(f + g)(x) = -x^2 - 11x

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