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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\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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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\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. Multiply Functions: We have:\newlinef(x)=5xf(x) = 5x\newlineg(x)=−2x+1g(x) = -2x + 1\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(5x)∗(−2x+1)(f * g)(x) = (5x) * (-2x + 1)
  3. Distribute 5x5x: Distribute 5x5x across the terms in g(x)g(x).
    (f⋅g)(x)=5x⋅(−2x)+5x⋅1(f \cdot g)(x) = 5x \cdot (-2x) + 5x \cdot 1
    (f⋅g)(x)=−10x2+5x(f \cdot g)(x) = -10x^2 + 5x

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