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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x+1f(x) = -2x + 1\newlineg(x)=5xg(x) = 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)=−2x+1f(x) = -2x + 1\newlineg(x)=5xg(x) = 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)=−2x+1f(x) = -2x + 1\newlineg(x)=5xg(x) = 5x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−2x+1)∗(5x)(f * g)(x) = (-2x + 1) * (5x)
  3. Distribute terms: Distribute the terms of the first function over the second function.\newline(f∗g)(x)=(−2x∗5x)+(1∗5x)(f * g)(x) = (-2x * 5x) + (1 * 5x)
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=−10x2+5x(f \cdot g)(x) = -10x^2 + 5x

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