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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4x+3f(x) = 4x + 3\newlineg(x)=3x2g(x) = 3x^2\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)=4x+3f(x) = 4x + 3\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. Given functions: We have:\newlinef(x)=4x+3f(x) = 4x + 3\newlineg(x)=3x2g(x) = 3x^2\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)=(4x+3)∗(3x2)(f * g)(x) = (4x + 3) * (3x^2)
  3. Distribute terms: Distribute 4x4x and 33 across 3x23x^2.\newline(f∗g)(x)=4x∗3x2+3∗3x2(f * g)(x) = 4x * 3x^2 + 3 * 3x^2
  4. Perform multiplication: Perform the multiplication.\newline(f⋅g)(x)=12x3+9x2(f \cdot g)(x) = 12x^3 + 9x^2

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