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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3x2f(x) = 3x^2\newlineg(x)=−2x+1g(x) = -2x + 1\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)=3x2f(x) = 3x^2\newlineg(x)=−2x+1g(x) = -2x + 1\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)=3x2f(x) = 3x^2\newlineg(x)=−2x+1g(x) = -2x + 1\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x2)∗(−2x+1)(f * g)(x) = (3x^2) * (-2x + 1)
  3. Distribute terms: Distribute 3x23x^2 to both terms in g(x)g(x).$(f∗g)(x)=3x2∗(−2x)+3x2∗1\$(f * g)(x) = 3x^2 * (-2x) + 3x^2 * 1
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=−6x3+3x2(f \cdot g)(x) = -6x^3 + 3x^2

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