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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4x+4f(x) = 4x + 4\newlineg(x)=−2x2g(x) = -2x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4x+4f(x) = 4x + 4\newlineg(x)=−2x2g(x) = -2x^2\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. Given Functions: We have:\newlinef(x)=4x+4f(x) = 4x + 4\newlineg(x)=−2x2g(x) = -2x^2\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)=(4x+4)∗(−2x2)(f * g)(x) = (4x + 4) * (-2x^2)
  3. Multiply Functions: Distribute −2x2-2x^2 to each term in 4x+44x + 4.
    (f∗g)(x)=4x∗(−2x2)+4∗(−2x2)(f * g)(x) = 4x * (-2x^2) + 4 * (-2x^2)
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=−8x3−8x2(f * g)(x) = -8x^3 - 8x^2

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