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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=x+4g(x) = x + 4\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)=−3xf(x) = -3x\newlineg(x)=x+4g(x) = x + 4\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)=−3xf(x) = -3x \newlineg(x)=x+4g(x) = x + 4 \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)=(−3x)∗(x+4)(f * g)(x) = (-3x) * (x + 4)
  3. Distribute −3x-3x: Now, distribute −3x-3x to both terms in the parentheses.\newline(f⋅g)(x)=−3x⋅x+(−3x)⋅4(f \cdot g)(x) = -3x \cdot x + (-3x) \cdot 4
  4. Perform multiplication: Perform the multiplication. (f∗g)(x)=−3x2−12x(f * g)(x) = -3x^2 - 12x

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