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What is (f−g)(x)(f - g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=3x2−3g(x) = 3x^2 - 3\newlineWrite your answer as a polynomial or a rational function in simplest form.

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Full solution

Q. What is (f−g)(x)(f - g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=3x2−3g(x) = 3x^2 - 3\newlineWrite your answer as a polynomial or a rational function in simplest form.
  1. Identify Formula: Identify the formula for (f−g)(x)(f - g)(x). The correct formula is (f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x).
  2. Substitute Values: We have f(x)=4xf(x) = 4x and g(x)=3x2−3g(x) = 3x^2 - 3. Substitute these values into the formula to get (f−g)(x)=4x−(3x2−3)(f - g)(x) = 4x - (3x^2 - 3).
  3. Simplify Equation: Simplify the equation (f−g)(x)=4x−(3x2−3)(f - g)(x) = 4x - (3x^2 - 3) to find (f−g)(x)(f - g)(x).(f−g)(x)=4x−3x2+3(f - g)(x) = 4x - 3x^2 + 3 (Note that we distribute the negative sign across the terms in the parentheses).
  4. Rearrange Terms: Rearrange the terms in descending order of the power of xx to write the polynomial in standard form.(f−g)(x)=−3x2+4x+3(f - g)(x) = -3x^2 + 4x + 3

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