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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5xf(x) = -5x\newlineg(x)=3x+1g(x) = 3x + 1\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)=−5xf(x) = -5x\newlineg(x)=3x+1g(x) = 3x + 1\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)=−5xf(x) = -5x\newlineg(x)=3x+1g(x) = 3x + 1\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−5x)∗(3x+1)(f * g)(x) = (-5x) * (3x + 1)
  3. Distribute −5x-5x: Distribute −5x-5x across the terms in the parentheses.\newline(f⋅g)(x)=(−5x⋅3x)+(−5x⋅1)(f \cdot g)(x) = (-5x \cdot 3x) + (-5x \cdot 1)
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=−15x2−5x(f \cdot g)(x) = -15x^2 - 5x

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