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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−3x2f(x) = -3x^2\newlineg(x)=−3x+3g(x) = -3x + 3\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)=−3x+3g(x) = -3x + 3\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)=−3x+3g(x) = -3x + 3 \newlineSubstitute the given 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)=(−3x2)−(−3x+3)(f - g)(x) = (-3x^2) - (-3x + 3)
  3. Simplify expression: Simplify the expression by distributing the negative sign and combining like terms. \newline(f−g)(x)=−3x2+3x−3(f - g)(x) = -3x^2 + 3x - 3

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