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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+1f(x) = -5x + 1\newlineg(x)=3xg(x) = 3x\newlineWrite your answer as a polynomial or a rational function in simplest form.

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Full solution

Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−5x+1f(x) = -5x + 1\newlineg(x)=3xg(x) = 3x\newlineWrite your answer as a polynomial or a rational function in simplest form.
  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)=3xg(x) = 3x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−5x+1)∗(3x)(f * g)(x) = (-5x + 1) * (3x)
  3. Distribute terms: Distribute each term in the first polynomial by each term in the second polynomial.\newline(f∗g)(x)=(−5x∗3x)+(1∗3x)(f * g)(x) = (-5x * 3x) + (1 * 3x)
  4. Perform multiplication: Perform the multiplication.\newline(f⋅g)(x)=−15x2+3x(f \cdot g)(x) = -15x^2 + 3x

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