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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=2x2−5xg(x) = 2x^2 - 5x\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)=−xf(x) = -x\newlineg(x)=2x2−5xg(x) = 2x^2 - 5x\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)=−xf(x) = -x\newlineg(x)=2x2−5xg(x) = 2x^2 - 5x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x)∗(2x2−5x)(f * g)(x) = (-x) * (2x^2 - 5x)
  3. Multiply Functions: Distribute −x-x across the terms in g(x)g(x).(f∗g)(x)=(−x)∗2x2+(−x)∗(−5x)(f * g)(x) = (-x) * 2x^2 + (-x) * (-5x)
  4. Distribute −x-x: Perform the multiplication.\newline(f⋅g)(x)=−2x3+5x2(f \cdot g)(x) = -2x^3 + 5x^2

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