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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=5xf(x) = 5x\newlineg(x)=−5x+1g(x) = -5x + 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)=−5x+1g(x) = -5x + 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. Calculate Product: We have:\newlinef(x)=5xf(x) = 5x\newlineg(x)=−5x+1g(x) = -5x + 1\newlineNow, calculate the product of f(x)f(x) and g(x)g(x).\newline(f∗g)(x)=(5x)∗(−5x+1)(f * g)(x) = (5x) * (-5x + 1)
  3. Distribute Terms: Distribute 5x5x across the terms in g(x)g(x). \newline(f⋅g)(x)=5x⋅(−5x)+5x⋅1(f \cdot g)(x) = 5x \cdot (-5x) + 5x \cdot 1
  4. Perform Multiplication: Perform the multiplication.\newline(f⋅g)(x)=−25x2+5x(f \cdot g)(x) = -25x^2 + 5x
  5. Final Answer: There are no like terms to combine, so the expression is already in its simplest form.\newlineThe final answer is (f∗g)(x)=−25x2+5x(f * g)(x) = -25x^2 + 5x.

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