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

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

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