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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=x2−4g(x) = x^2 - 4\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)=2xf(x) = 2x\newlineg(x)=x2−4g(x) = x^2 - 4\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). 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)=2xf(x) = 2x and g(x)=x2−4g(x) = x^2 - 4. Substitute these values into the formula to get (f∗g)(x)=(2x)∗(x2−4)(f * g)(x) = (2x) * (x^2 - 4).
  3. Simplify Equation: Simplify the equation (f∗g)(x)=(2x)∗(x2−4)(f * g)(x) = (2x) * (x^2 - 4) to find (f∗g)(x)(f * g)(x).
    (f∗g)(x)=2x(x2)−2x(4)(f * g)(x) = 2x(x^2) - 2x(4)
    (f∗g)(x)=2x3−8x(f * g)(x) = 2x^3 - 8x

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