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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2xf(x) = -2x\newlineg(x)=−x+5g(x) = -x + 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)=−2xf(x) = -2x\newlineg(x)=−x+5g(x) = -x + 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)=−2xf(x) = -2x\newlineg(x)=−x+5g(x) = -x + 5\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−2x)∗(−x+5)(f * g)(x) = (-2x) * (-x + 5)
  3. Distribute −2x-2x: Distribute −2x-2x to both terms in the parentheses.\newline(f⋅g)(x)=(−2x)⋅(−x)+(−2x)⋅5(f \cdot g)(x) = (-2x) \cdot (-x) + (-2x) \cdot 5
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=2x2−10x(f \cdot g)(x) = 2x^2 - 10x

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