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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=−3x2+7xg(x) = -3x^2 + 7x\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)=−4xf(x) = -4x\newlineg(x)=−3x2+7xg(x) = -3x^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).(f−g)(x)(f - g)(x) is the difference 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. Substitute functions: We have: \newlinef(x)=−4xf(x) = -4x \newlineg(x)=−3x2+7xg(x) = -3x^2 + 7x \newlineSubstitute the functions into the formula for (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)=(−4x)−(−3x2+7x)(f - g)(x) = (-4x) - (-3x^2 + 7x)
  3. Distribute negative sign: Distribute the negative sign through the terms in g(x)g(x).(f−g)(x)=−4x−(−3x2)−7x(f - g)(x) = -4x - (-3x^2) - 7x(f−g)(x)=−4x+3x2−7x(f - g)(x) = -4x + 3x^2 - 7x
  4. Combine like terms: Combine like terms. Since there are no like terms with 3x23x^2, it remains as is. Combine the terms −4x-4x and −7x-7x. (f−g)(x)=3x2−4x−7x(f - g)(x) = 3x^2 - 4x - 7x (f−g)(x)=3x2−11x(f - g)(x) = 3x^2 - 11x

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