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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2+3f(x) = -3x^2 + 3\newlineg(x)=4xg(x) = 4x\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)=−3x2+3f(x) = -3x^2 + 3\newlineg(x)=4xg(x) = 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 product 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. Given Functions: We have: \newlinef(x)=−3x2+3f(x) = -3x^2 + 3 \newlineg(x)=4xg(x) = 4x \newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−3x2+3)∗(4x)(f * g)(x) = (-3x^2 + 3) * (4x)
  3. Multiply Functions: Distribute 4x4x to each term in f(x)f(x).
    (f∗g)(x)=−3x2∗4x+3∗4x(f * g)(x) = -3x^2 * 4x + 3 * 4x
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=−12x3+12x(f * g)(x) = -12x^3 + 12x

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