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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x+1f(x) = -3x + 1\newlineg(x)=−3x2g(x) = -3x^2\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)=−3x+1f(x) = -3x + 1\newlineg(x)=−3x2g(x) = -3x^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. Calculate Product: We have:\newlinef(x)=−3x+1f(x) = -3x + 1\newlineg(x)=−3x2g(x) = -3x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−3x+1)∗(−3x2)(f * g)(x) = (-3x + 1) * (-3x^2)
  3. Distribute Terms: Distribute each term in the first polynomial by each term in the second polynomial.\newline(f∗g)(x)=(−3x∗−3x2)+(1∗−3x2)(f * g)(x) = (-3x * -3x^2) + (1 * -3x^2)\newline(f∗g)(x)=9x3−3x2(f * g)(x) = 9x^3 - 3x^2

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