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What is (f+g)(x)(f + g)(x)?\newlinef(x)=2x2−6xf(x) = 2x^2 - 6x\newlineg(x)=−x2g(x) = -x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

Full solution

Q. What is (f+g)(x)(f + g)(x)?\newlinef(x)=2x2−6xf(x) = 2x^2 - 6x\newlineg(x)=−x2g(x) = -x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Define functions: (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)=2x2−6xf(x) = 2x^2 - 6x\newlineg(x)=−x2g(x) = -x^2\newlineNow we will add these two functions together.\newline(f+g)(x)=(2x2−6x)+(−x2)(f + g)(x) = (2x^2 - 6x) + (-x^2)
  3. Combine like terms: Combine like terms to simplify the expression.\newline(f+g)(x)=2x2−6x−x2(f + g)(x) = 2x^2 - 6x - x^2\newline(f+g)(x)=(2x2−x2)−6x(f + g)(x) = (2x^2 - x^2) - 6x\newline(f+g)(x)=x2−6x(f + g)(x) = x^2 - 6x

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