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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=2x2+3xg(x) = 2x^2 + 3x\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)=4xf(x) = 4x\newlineg(x)=2x2+3xg(x) = 2x^2 + 3x\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)=4xf(x) = 4x\newlineg(x)=2x2+3xg(x) = 2x^2 + 3x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(4x)∗(2x2+3x)(f * g)(x) = (4x) * (2x^2 + 3x)
  3. Multiply functions: Distribute 4x4x across the terms in g(x)g(x).
    (f∗g)(x)=4x∗2x2+4x∗3x(f * g)(x) = 4x * 2x^2 + 4x * 3x
  4. Distribute 4x4x: Perform the multiplication for each term.(f⋅g)(x)=8x3+12x2(f \cdot g)(x) = 8x^3 + 12x^2

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