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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=4x+1g(x) = 4x + 1\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)=x2f(x) = x^2\newlineg(x)=4x+1g(x) = 4x + 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. Define functions: We have:\newlinef(x)=x2f(x) = x^2\newlineg(x)=4x+1g(x) = 4x + 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)=x2∗(4x+1)(f * g)(x) = x^2 * (4x + 1)
  3. Multiply functions: Distribute x2x^2 to each term in g(x)g(x).(f∗g)(x)=x2∗4x+x2∗1(f * g)(x) = x^2 * 4x + x^2 * 1
  4. Distribute terms: Perform the multiplication.\newline(f∗g)(x)=4x3+x2(f * g)(x) = 4x^3 + x^2

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