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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=−2x2−3xg(x) = -2x^2 - 3x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=−2x2−3xg(x) = -2x^2 - 3x\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)=−2x2−3xg(x) = -2x^2 - 3x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(4x)∗(−2x2−3x)(f * g)(x) = (4x) * (-2x^2 - 3x)
  3. Distribute 4x4x: Distribute 4x4x across the terms in g(x)g(x).
    (f⋅g)(x)=4x⋅(−2x2)+4x⋅(−3x)(f \cdot g)(x) = 4x \cdot (-2x^2) + 4x \cdot (-3x)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=−8x3−12x2(f \cdot g)(x) = -8x^3 - 12x^2

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