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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______\newline

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Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______\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. Subtract Functions: We have: \newlinef(x)=−xf(x) = -x \newlineg(x)=3x2−6xg(x) = 3x^2 - 6x\newlineNow, we need to subtract g(x)g(x) from f(x)f(x) to find (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)=(−x)−(3x2−6x)(f - g)(x) = (-x) - (3x^2 - 6x)
  3. Distribute Negative Sign: Distribute the negative sign through the parentheses to subtract g(x)g(x) from f(x)f(x).(f−g)(x)=−x−3x2+6x(f - g)(x) = -x - 3x^2 + 6x
  4. Combine Like Terms: Combine like terms to simplify the expression.\newline(f−g)(x)=−3x2+6x−x(f - g)(x) = -3x^2 + 6x - x\newline(f−g)(x)=−3x2+5x(f - g)(x) = -3x^2 + 5x

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