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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x2f(x) = -2x^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

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x2f(x) = -2x^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)=−2x2f(x) = -2x^2\newlineg(x)=2x+1g(x) = 2x + 1\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)=(−2x2)∗(2x+1)(f * g)(x) = (-2x^2) * (2x + 1)
  3. Multiply functions: Distribute −2x2-2x^2 to each term in the binomial (2x+1)(2x + 1).(f∗g)(x)=(−2x2∗2x)+(−2x2∗1)(f * g)(x) = (-2x^2 * 2x) + (-2x^2 * 1)
  4. Distribute terms: Perform the multiplication for each term.\newline(f∗g)(x)=−4x3−2x2(f * g)(x) = -4x^3 - 2x^2

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