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What is (f+g)(x)(f + g)(x)?\newlinef(x)=−x2−9xf(x) = -x^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)=−x2−9xf(x) = -x^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. Find f+gf + g: We have:\newlinef(x)=−x2−9xf(x) = -x^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)=(−x2−9x)+(x2)(f + g)(x) = (-x^2 - 9x) + (x^2)
  3. Perform addition: Perform the addition of the two polynomials.\newline(f+g)(x)=−x2−9x+x2(f + g)(x) = -x^2 - 9x + x^2\newlineNow, combine like terms.\newline(f+g)(x)=(−x2+x2)−9x(f + g)(x) = (-x^2 + x^2) - 9x\newline(f+g)(x)=0−9x(f + g)(x) = 0 - 9x\newline(f+g)(x)=−9x(f + g)(x) = -9x

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