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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=2x+2g(x) = 2x + 2\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)=3xf(x) = 3x\newlineg(x)=2x+2g(x) = 2x + 2\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. Multiply Functions: We have: \newlinef(x)=3xf(x) = 3x \newlineg(x)=2x+2g(x) = 2x + 2 \newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x)∗(2x+2)(f * g)(x) = (3x) * (2x + 2)
  3. Distribute 3x3x: Distribute 3x3x across the terms in g(x)g(x).(f⋅g)(x)=3x⋅2x+3x⋅2(f \cdot g)(x) = 3x \cdot 2x + 3x \cdot 2
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=6x2+6x(f \cdot g)(x) = 6x^2 + 6x
  5. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 6x2+6x6x^2 + 6x is already in its simplest form.

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