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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x+4f(x) = -2x + 4\newlineg(x)=x2g(x) = x^2\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)=x2g(x) = x^2\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)=x2g(x) = x^2\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−2x+4)∗(x2)(f * g)(x) = (-2x + 4) * (x^2)
  3. Distribute Terms: Distribute x2x^2 to each term in f(x)f(x).$(f∗g)(x)=(−2x∗x2)+(4∗x2)\$(f * g)(x) = (-2x * x^2) + (4 * x^2)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=−2x3+4x2(f \cdot g)(x) = -2x^3 + 4x^2

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