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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x+4f(x) = -3x + 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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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x+4f(x) = -3x + 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. Define Functions: We have:\newlinef(x)=−3x+4f(x) = -3x + 4\newlineg(x)=−x2g(x) = -x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−3x+4)∗(−x2)(f * g)(x) = (-3x + 4) * (-x^2)
  3. Multiply Functions: Distribute each term in f(x)f(x) by each term in g(x)g(x) to find the product.(f∗g)(x)=(−3x)(−x2)+(4)(−x2)(f * g)(x) = (-3x)(-x^2) + (4)(-x^2)
  4. Distribute Terms: Perform the multiplication for each term.\newline(f∗g)(x)=3x3−4x2(f * g)(x) = 3x^3 - 4x^2

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