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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=−x+4g(x) = -x + 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)=x2f(x) = x^2\newlineg(x)=−x+4g(x) = -x + 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).(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. Find Functions: We have: \newlinef(x)=x2f(x) = x^2 \newlineg(x)=−x+4g(x) = -x + 4 \newlineWhich function represents (f∗g)(x)(f * g)(x)?\newline(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)\newline(f∗g)(x)=x2∗(−x+4)(f * g)(x) = x^2 * (-x + 4)
  3. Distribute x2x^2: Distribute x2x^2 to each term in (−x+4)(-x + 4).
    (f∗g)(x)=x2∗(−x)+x2∗4(f * g)(x) = x^2 * (-x) + x^2 * 4
    (f∗g)(x)=−x3+4x2(f * g)(x) = -x^3 + 4x^2

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