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

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