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What is (f∗g)(x)(f * g)(x)? f(x)=3x2+9xf(x) = 3x^2 + 9x g(x)=3xg(x) = 3x Write your answer as a polynomial or a rational function in simplest form. ______

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Q. What is (f∗g)(x)(f * g)(x)? f(x)=3x2+9xf(x) = 3x^2 + 9x g(x)=3xg(x) = 3x Write your answer as a polynomial or a rational function in simplest form. ______
  1. Identify formula: Identify the formula for the product of two functions, which is (f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x).
  2. Substitute functions: Given f(x)=3x2+9xf(x) = 3x^2 + 9x and g(x)=3xg(x) = 3x, substitute these functions into the formula to get (f∗g)(x)=(3x2+9x)∗3x(f * g)(x) = (3x^2 + 9x) * 3x.
  3. Simplify equation: Simplify the equation (f∗g)(x)=(3x2+9x)∗3x(f * g)(x) = (3x^2 + 9x) * 3x by distributing 3x3x across the terms in the parentheses.\newline(f∗g)(x)=3x2∗3x+9x∗3x(f * g)(x) = 3x^2 * 3x + 9x * 3x
  4. Perform multiplication: Perform the multiplication for each term.\newline(f∗g)(x)=9x3+27x2(f * g)(x) = 9x^3 + 27x^2

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