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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=2x2−6xg(x) = 2x^2 - 6x\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)=3xf(x) = 3x\newlineg(x)=2x2−6xg(x) = 2x^2 - 6x\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. Define Functions: We have:\newlinef(x)=3xf(x) = 3x\newlineg(x)=2x2−6xg(x) = 2x^2 - 6x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x)∗(2x2−6x)(f * g)(x) = (3x) * (2x^2 - 6x)
  3. Multiply Functions: Distribute 3x3x to each term in g(x)g(x).
    (f∗g)(x)=3x∗2x2−3x∗6x(f * g)(x) = 3x * 2x^2 - 3x * 6x
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=6x3−18x2(f * g)(x) = 6x^3 - 18x^2
  5. Perform Multiplication: Check for any like terms that can be combined.\newlineThere are no like terms in 6x3−18x26x^3 - 18x^2, so this is the simplest form.

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