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What is (f−g)(x)(f - g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=2x2+7xg(x) = 2x^2 + 7x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=2x2+7xg(x) = 2x^2 + 7x\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). \newline(f−g)(x)(f - g)(x) is the difference of f(x)f(x) and g(x)g(x), which means we subtract g(x)g(x) from f(x)f(x).\newline(f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x)
  2. Substitute Functions: Substitute the given functions into the formula.\newlinef(x)=x2f(x) = x^2\newlineg(x)=2x2+7xg(x) = 2x^2 + 7x\newline(f−g)(x)=x2−(2x2+7x)(f - g)(x) = x^2 - (2x^2 + 7x)
  3. Distribute and Combine: Distribute the negative sign and combine like terms.\newline(f−g)(x)=x2−2x2−7x(f - g)(x) = x^2 - 2x^2 - 7x\newline(f−g)(x)=−x2−7x(f - g)(x) = -x^2 - 7x

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