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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−4xf(x) = -4x\newlineg(x)=2x2+2xg(x) = 2x^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)=−4xf(x) = -4x\newlineg(x)=2x2+2xg(x) = 2x^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. Multiply functions: We have: \newlinef(x)=−4xf(x) = -4x \newlineg(x)=2x2+2xg(x) = 2x^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)=(−4x)∗(2x2+2x)(f * g)(x) = (-4x) * (2x^2 + 2x)
  3. Distribute −4x-4x: Distribute −4x-4x across the terms in g(x)g(x).(f∗g)(x)=(−4x∗2x2)+(−4x∗2x)(f * g)(x) = (-4x * 2x^2) + (-4x * 2x)
  4. Perform multiplication: Perform the multiplication.\newline(f⋅g)(x)=−8x3−8x2(f \cdot g)(x) = -8x^3 - 8x^2

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