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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=x2f(x) = x^2\newlineg(x)=x+6g(x) = x + 6\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)=x2f(x) = x^2\newlineg(x)=x+6g(x) = x + 6\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)=x2f(x) = x^2 \newlineg(x)=x+6g(x) = x + 6 \newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=x2∗(x+6)(f * g)(x) = x^2 * (x + 6)
  3. Distribute Terms: Distribute x2x^2 to both terms in the parentheses.\newline(f⋅g)(x)=x2⋅x+x2⋅6(f \cdot g)(x) = x^2 \cdot x + x^2 \cdot 6
  4. Simplify Expression: Simplify the expression by multiplying the terms. f \cdot g)(x) = x^\(3 + 66x^22\

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