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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5xf(x) = -5x\newlineg(x)=−3x2+9xg(x) = -3x^2 + 9x\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)=−5xf(x) = -5x\newlineg(x)=−3x2+9xg(x) = -3x^2 + 9x\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)=−5xf(x) = -5x\newlineg(x)=−3x2+9xg(x) = -3x^2 + 9x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−5x)∗(−3x2+9x)(f * g)(x) = (-5x) * (-3x^2 + 9x)
  3. Distribute −5x-5x: Distribute −5x-5x across the terms in g(x)g(x).(f⋅g)(x)=(−5x)⋅(−3x2)+(−5x)⋅(9x)(f \cdot g)(x) = (-5x) \cdot (-3x^2) + (-5x) \cdot (9x)
  4. Perform multiplication: Perform the multiplication. (f⋅g)(x)=15x3−45x2(f \cdot g)(x) = 15x^3 - 45x^2

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