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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=4x+6g(x) = 4x + 6\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)=4x+6g(x) = 4x + 6\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)=4x+6g(x) = 4x + 6 \newlineWhich function represents (f∗g)(x)(f * g)(x)?\newline(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)\newline(f∗g)(x)=(−x)∗(4x+6)(f * g)(x) = (-x) * (4x + 6)
  3. Distribute −x-x: We found: \newline(f∗g)(x)=(−x)∗(4x+6)(f * g)(x) = (-x) * (4x + 6) \newlineNow, distribute −x-x to both terms in the parentheses.\newline(f∗g)(x)=−x∗4x+(−x)∗6(f * g)(x) = -x * 4x + (-x) * 6
  4. Perform Multiplication: Perform the multiplication:\newline(f⋅g)(x)=−4x2−6x(f \cdot g)(x) = -4x^2 - 6x\newlineExpress your answer as a simplified polynomial.

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