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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+1f(x) = -5x + 1\newlineg(x)=4xg(x) = 4x\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)=−5x+1f(x) = -5x + 1\newlineg(x)=4xg(x) = 4x\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)=−5x+1f(x) = -5x + 1\newlineg(x)=4xg(x) = 4x\newlineTo find (f∗g)(x)(f * g)(x), we need to multiply f(x)f(x) by g(x)g(x).\newline(f∗g)(x)=(−5x+1)∗(4x)(f * g)(x) = (-5x + 1) * (4x)
  3. Distribute Terms: Distribute 4x4x to each term in (−5x+1)(-5x + 1).
    (f∗g)(x)=(−5x∗4x)+(1∗4x)(f * g)(x) = (-5x * 4x) + (1 * 4x)
  4. Perform Multiplication: Perform the multiplication. (f⋅g)(x)=−20x2+4x(f \cdot g)(x) = -20x^2 + 4x

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