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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=5x+3g(x) = 5x + 3\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2xf(x) = 2x\newlineg(x)=5x+3g(x) = 5x + 3\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. Find f∗gf * g: We have:\newlinef(x)=2xf(x) = 2x\newlineg(x)=5x+3g(x) = 5x + 3\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)=(2x)∗(5x+3)(f * g)(x) = (2x) * (5x + 3)
  3. Distribute 2x2x: Distribute 2x2x across the terms in g(x)g(x).
    (f⋅g)(x)=2x⋅5x+2x⋅3(f \cdot g)(x) = 2x \cdot 5x + 2x \cdot 3
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=10x2+6x(f \cdot g)(x) = 10x^2 + 6x

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