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

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Q. What is (fg)(x)(f * g)(x)?\newlinef(x)=x+2f(x) = -x + 2\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 (fg)(x)(f * g)(x).(fg)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(fg)(x)=f(x)g(x)(f * g)(x) = f(x) * g(x)
  2. Multiply functions: We have: \newlinef(x)=x+2f(x) = -x + 2 \newlineg(x)=3xg(x) = 3x \newlineNow, we need to multiply these two functions to find (fg)(x)(f * g)(x).\newline(fg)(x)=(x+2)(3x)(f * g)(x) = (-x + 2) * (3x)
  3. Distribute terms: Distribute 3x3x to each term in the first polynomial.\newline(fg)(x)=(x3x)+(23x)(f \cdot g)(x) = (-x \cdot 3x) + (2 \cdot 3x)
  4. Perform multiplication: Perform the multiplication.\newline(fg)(x)=3x2+6x(f \cdot g)(x) = -3x^2 + 6x

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