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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4x+3f(x) = 4x + 3\newlineg(x)=−4xg(x) = -4x\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)=4x+3f(x) = 4x + 3\newlineg(x)=−4xg(x) = -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. Define Functions: We have:\newlinef(x)=4x+3f(x) = 4x + 3\newlineg(x)=−4xg(x) = -4x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(4x+3)∗(−4x)(f * g)(x) = (4x + 3) * (-4x)
  3. Multiply Functions: Distribute −4x-4x to each term in the parentheses.\newline(f∗g)(x)=4x∗(−4x)+3∗(−4x)(f * g)(x) = 4x * (-4x) + 3 * (-4x)
  4. Distribute Terms: Perform the multiplication.\newline(f∗g)(x)=−16x2−12x(f * g)(x) = -16x^2 - 12x
  5. Perform Multiplication: There are no like terms to combine, so the expression is already in its simplest form.\newlineThe final answer is (f⋅g)(x)=−16x2−12x(f \cdot g)(x) = -16x^2 - 12x.

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