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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=−3x2+6xg(x) = -3x^2 + 6x\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)=5xf(x) = 5x\newlineg(x)=−3x2+6xg(x) = -3x^2 + 6x\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. Calculate product: We have:\newlinef(x)=5xf(x) = 5x\newlineg(x)=−3x2+6xg(x) = -3x^2 + 6x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(5x)∗(−3x2+6x)(f * g)(x) = (5x) * (-3x^2 + 6x)
  3. Distribute f(x)f(x): Distribute f(x)f(x) across g(x)g(x).
    (f⋅g)(x)=5x⋅(−3x2)+5x⋅(6x)(f \cdot g)(x) = 5x \cdot (-3x^2) + 5x \cdot (6x)
    (f⋅g)(x)=−15x3+30x2(f \cdot g)(x) = -15x^3 + 30x^2

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