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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x+2f(x) = 3x + 2\newlineg(x)=xg(x) = x\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)=3x+2f(x) = 3x + 2\newlineg(x)=xg(x) = x\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. Calculate Product: We have:\newlinef(x)=3x+2f(x) = 3x + 2\newlineg(x)=xg(x) = x\newlineNow, calculate the product of f(x)f(x) and g(x)g(x) to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x+2)∗x(f * g)(x) = (3x + 2) * x
  3. Distribute xx: Distribute xx across the terms in the parentheses.\newline(f⋅g)(x)=3x⋅x+2⋅x(f \cdot g)(x) = 3x \cdot x + 2 \cdot x
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=3x2+2x(f \cdot g)(x) = 3x^2 + 2x

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