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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=−2x2−4xg(x) = -2x^2 - 4x\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)=−xf(x) = -x\newlineg(x)=−2x2−4xg(x) = -2x^2 - 4x\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. Calculate product: We have:\newlinef(x)=−xf(x) = -x\newlineg(x)=−2x2−4xg(x) = -2x^2 - 4x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x)∗(−2x2−4x)(f * g)(x) = (-x) * (-2x^2 - 4x)
  3. Distribute and simplify: Distribute f(x)f(x) across g(x)g(x).
    (f⋅g)(x)=(−x)⋅(−2x2)+(−x)⋅(−4x)(f \cdot g)(x) = (-x) \cdot (-2x^2) + (-x) \cdot (-4x)
    (f⋅g)(x)=2x3+4x2(f \cdot g)(x) = 2x^3 + 4x^2

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