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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3xf(x) = -3x\newlineg(x)=x2+xg(x) = x^2 + x\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)=−3xf(x) = -3x\newlineg(x)=x2+xg(x) = x^2 + x\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)=−3xf(x) = -3x \newlineg(x)=x2+xg(x) = x^2 + x \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)=(−3x)∗(x2+x)(f * g)(x) = (-3x) * (x^2 + x)
  3. Multiply functions: Distribute −3x-3x to both terms in the parentheses.\newline(f∗g)(x)=(−3x)∗x2+(−3x)∗x(f * g)(x) = (-3x) * x^2 + (-3x) * x
  4. Distribute terms: Multiply the terms.\newline(f∗g)(x)=−3x3−3x2(f * g)(x) = -3x^3 - 3x^2

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