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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+5f(x) = 3x + 5\newlineg(x)=−5xg(x) = -5x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+5f(x) = 3x + 5\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. Define functions: We have:\newlinef(x)=3x+5f(x) = 3x + 5\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)=(3x+5)∗(−5x)(f * g)(x) = (3x + 5) * (-5x)
  3. Multiply functions: Distribute −5x-5x to both terms in the parentheses.\newline(f∗g)(x)=3x∗(−5x)+5∗(−5x)(f * g)(x) = 3x * (-5x) + 5 * (-5x)
  4. Distribute terms: Perform the multiplication.\newline(f⋅g)(x)=−15x2−25x(f \cdot g)(x) = -15x^2 - 25x

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