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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−3x2+4xg(x) = -3x^2 + 4x\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)=−3x2f(x) = -3x^2\newlineg(x)=−3x2+4xg(x) = -3x^2 + 4x\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)=−3x2f(x) = -3x^2\newlineg(x)=−3x2+4xg(x) = -3x^2 + 4x\newlineSubstitute these functions into the formula for (f−g)(x)(f - g)(x).\newline(f−g)(x)=(−3x2)−(−3x2+4x)(f - g)(x) = (-3x^2) - (-3x^2 + 4x)
  3. Distribute and Combine: Distribute the negative sign through the terms of g(x)g(x) and combine like terms.(f−g)(x)=−3x2−(−3x2)−4x(f - g)(x) = -3x^2 - (-3x^2) - 4x(f−g)(x)=−3x2+3x2−4x(f - g)(x) = -3x^2 + 3x^2 - 4x(f−g)(x)=−4x(f - g)(x) = -4x

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