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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5xf(x) = -5x\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)=−5xf(x) = -5x\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)=−5xf(x) = -5x and g(x)=x2−4g(x) = x^2 - 4. Substitute these values into the formula to get (f∗g)(x)=(−5x)∗(x2−4)(f * g)(x) = (-5x) * (x^2 - 4).
  3. Simplify Equation: Simplify the equation (f∗g)(x)=(−5x)∗(x2−4)(f * g)(x) = (-5x) * (x^2 - 4) to find (f∗g)(x)(f * g)(x).
    (f∗g)(x)=−5x∗x2−(−5x)∗4(f * g)(x) = -5x * x^2 - (-5x) * 4
    (f∗g)(x)=−5x3+20x(f * g)(x) = -5x^3 + 20x

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