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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=3x2+7xg(x) = 3x^2 + 7x\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=4xf(x) = 4x\newlineg(x)=3x2+7xg(x) = 3x^2 + 7x\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)=4xf(x) = 4x\newlineg(x)=3x2+7xg(x) = 3x^2 + 7x\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∗(3x2+7x)(f * g)(x) = 4x * (3x^2 + 7x)
  3. Distribute 4x4x: Distribute 4x4x across the terms in g(x)g(x).(f∗g)(x)=4x∗3x2+4x∗7x(f * g)(x) = 4x * 3x^2 + 4x * 7x
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=12x3+28x2(f \cdot g)(x) = 12x^3 + 28x^2

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