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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−2x2−9xf(x) = -2x^2 - 9x\newlineg(x)=5xg(x) = 5x\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)=−2x2−9xf(x) = -2x^2 - 9x\newlineg(x)=5xg(x) = 5x\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)=−2x2−9xf(x) = -2x^2 - 9x\newlineg(x)=5xg(x) = 5x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−2x2−9x)∗(5x)(f * g)(x) = (-2x^2 - 9x) * (5x)
  3. Multiply Functions: Distribute 5x5x to each term in the polynomial −2x2−9x-2x^2 - 9x.
    (f∗g)(x)=(−2x2∗5x)+(−9x∗5x)(f * g)(x) = (-2x^2 * 5x) + (-9x * 5x)
  4. Distribute Terms: Perform the multiplication for each term.\newline(f∗g)(x)=−10x3−45x2(f * g)(x) = -10x^3 - 45x^2

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