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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x+4f(x) = 2x + 4\newlineg(x)=−3xg(x) = -3x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x+4f(x) = 2x + 4\newlineg(x)=−3xg(x) = -3x\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)=2x+4f(x) = 2x + 4 \newlineg(x)=−3xg(x) = -3x \newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(2x+4)∗(−3x)(f * g)(x) = (2x + 4) * (-3x)
  3. Distribute Terms: Distribute −3x-3x to each term in the polynomial 2x+42x + 4.\newline(f∗g)(x)=2x∗(−3x)+4∗(−3x)(f * g)(x) = 2x * (-3x) + 4 * (-3x)
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−6x2−12x(f \cdot g)(x) = -6x^2 - 12x

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