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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=2x2+8xg(x) = 2x^2 + 8x\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)=2x2+8xg(x) = 2x^2 + 8x\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)=2x2+8xg(x) = 2x^2 + 8x\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(2x)∗(2x2+8x)(f * g)(x) = (2x) * (2x^2 + 8x)
  3. Multiply functions: Distribute 2x2x across the terms in g(x)g(x).
    (f∗g)(x)=2x∗2x2+2x∗8x(f * g)(x) = 2x * 2x^2 + 2x * 8x
  4. Distribute terms: Perform the multiplication.\newline(f∗g)(x)=4x3+16x2(f * g)(x) = 4x^3 + 16x^2

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