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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=2x2+4xg(x) = 2x^2 + 4x\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)=2xf(x) = 2x\newlineg(x)=2x2+4xg(x) = 2x^2 + 4x\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)=2xf(x) = 2x\newlineg(x)=2x2+4xg(x) = 2x^2 + 4x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(2x)∗(2x2+4x)(f * g)(x) = (2x) * (2x^2 + 4x)
  3. Distribute 2x2x: Distribute 2x2x across the terms in g(x)g(x).
    (f⋅g)(x)=2x⋅2x2+2x⋅4x(f \cdot g)(x) = 2x \cdot 2x^2 + 2x \cdot 4x
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=4x3+8x2(f \cdot g)(x) = 4x^3 + 8x^2

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