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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=xf(x) = x\newlineg(x)=x2−2xg(x) = x^2 - 2x\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)=xf(x) = x\newlineg(x)=x2−2xg(x) = x^2 - 2x\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)=xf(x) = x \newlineg(x)=x2−2xg(x) = x^2 - 2x \newlineNow, we need to multiply f(x)f(x) by g(x)g(x) to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=x∗(x2−2x)(f * g)(x) = x * (x^2 - 2x)
  3. Multiply Functions: Distribute xx across the terms in g(x)g(x).(f∗g)(x)=x∗x2−x∗2x(f * g)(x) = x * x^2 - x * 2x
  4. Distribute xx: Perform the multiplication.(f∗g)(x)=x3−2x2(f * g)(x) = x^3 - 2x^2

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