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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2+3xf(x) = x^2 + 3x\newlineg(x)=xg(x) = x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2+3xf(x) = x^2 + 3x\newlineg(x)=xg(x) = x\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)=x2+3xf(x) = x^2 + 3x\newlineg(x)=xg(x) = x\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+3x)∗x(f * g)(x) = (x^2 + 3x) * x
  3. Distribute xx: Distribute xx to each term in the polynomial x2+3xx^2 + 3x.\newline(f∗g)(x)=x∗x2+x∗3x(f * g)(x) = x * x^2 + x * 3x
  4. Perform multiplication: Perform the multiplication.\newline(f⋅g)(x)=x3+3x2(f \cdot g)(x) = x^3 + 3x^2

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