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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x+1f(x) = -3x + 1\newlineg(x)=−2xg(x) = -2x\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)=−3x+1f(x) = -3x + 1\newlineg(x)=−2xg(x) = -2x\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)=−3x+1f(x) = -3x + 1\newlineg(x)=−2xg(x) = -2x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−3x+1)∗(−2x)(f * g)(x) = (-3x + 1) * (-2x)
  3. Distribute Terms: Distribute each term in the first polynomial by each term in the second polynomial.\newline(f∗g)(x)=(−3x∗−2x)+(1∗−2x)(f * g)(x) = (-3x * -2x) + (1 * -2x)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=(6x2)+(−2x)(f \cdot g)(x) = (6x^2) + (-2x)
  5. Write Final Answer: Write the final answer as a simplified polynomial.\newline(f⋅g)(x)=6x2−2x(f \cdot g)(x) = 6x^2 - 2x

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