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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+5f(x) = 3x + 5\newlineg(x)=3x2g(x) = 3x^2\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)=3x+5f(x) = 3x + 5\newlineg(x)=3x2g(x) = 3x^2\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)=3x2g(x) = 3x^2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x+5)∗(3x2)(f * g)(x) = (3x + 5) * (3x^2)
  3. Multiply functions: Distribute 3x23x^2 to each term in 3x+53x + 5.
    (f∗g)(x)=3x∗3x2+5∗3x2(f * g)(x) = 3x * 3x^2 + 5 * 3x^2
  4. Distribute terms: Perform the multiplication.\newline(f∗g)(x)=9x3+15x2(f * g)(x) = 9x^3 + 15x^2

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