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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x+3f(x) = 2x + 3\newlineg(x)=−3x2g(x) = -3x^2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Add and subtract functionsright chevron icon

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=2x+3f(x) = 2x + 3\newlineg(x)=−3x2g(x) = -3x^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. Given functions: We have:\newlinef(x)=2x+3f(x) = 2x + 3\newlineg(x)=−3x2g(x) = -3x^2\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+3)∗(−3x2)(f * g)(x) = (2x + 3) * (-3x^2)
  3. Multiply functions: Distribute −3x2-3x^2 to each term in 2x+32x + 3.
    (f∗g)(x)=2x∗(−3x2)+3∗(−3x2)(f * g)(x) = 2x * (-3x^2) + 3 * (-3x^2)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=−6x3−9x2(f * g)(x) = -6x^3 - 9x^2

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