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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\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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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\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. Define product: We have:\newlinef(x)=2xf(x) = 2x\newlineg(x)=−x2+2xg(x) = -x^2 + 2x\newlineTo find (f∗g)(x)(f * g)(x), we multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(2x)∗(−x2+2x)(f * g)(x) = (2x) * (-x^2 + 2x)
  3. Multiply functions: Distribute 2x2x across the terms in g(x)g(x).
    (f∗g)(x)=2x∗(−x2)+2x∗(2x)(f * g)(x) = 2x * (-x^2) + 2x * (2x)
  4. Distribute terms: Perform the multiplication.\newline(f⋅g)(x)=−2x3+4x2(f \cdot g)(x) = -2x^3 + 4x^2

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