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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=xf(x) = x\newlineg(x)=3x2−3g(x) = 3x^2 - 3\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)=3x2−3g(x) = 3x^2 - 3\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)=xf(x) = x \newlineg(x)=3x2−3g(x) = 3x^2 - 3\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)=x∗(3x2−3)(f * g)(x) = x * (3x^2 - 3)
  3. Calculate Product: We found: \newline(f∗g)(x)=x∗(3x2−3)(f * g)(x) = x * (3x^2 - 3) \newlineExpress your answer as a simplified polynomial or rational function.\newlineDistribute the xx across the terms in the parentheses.\newline(f∗g)(x)=x∗3x2−x∗3(f * g)(x) = x * 3x^2 - x * 3
  4. Simplify Expression: Simplify the expression. \newline(f⋅g)(x)=3x3−3x(f \cdot g)(x) = 3x^3 - 3x

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