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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=−2x+6g(x) = -2x + 6\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−xf(x) = -x\newlineg(x)=−2x+6g(x) = -2x + 6\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. Multiply Functions: We have:\newlinef(x)=−xf(x) = -x\newlineg(x)=−2x+6g(x) = -2x + 6\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x)∗(−2x+6)(f * g)(x) = (-x) * (-2x + 6)
  3. Distribute −x-x: Distribute −x-x across the terms in g(x)g(x).(f⋅g)(x)=(−x)⋅(−2x)+(−x)⋅6(f \cdot g)(x) = (-x) \cdot (-2x) + (-x) \cdot 6
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=2x2−6x(f \cdot g)(x) = 2x^2 - 6x

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