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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−3x2+8xf(x) = -3x^2 + 8x\newlineg(x)=2xg(x) = 2x\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)=−3x2+8xf(x) = -3x^2 + 8x\newlineg(x)=2xg(x) = 2x\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. Define product: We have:\newlinef(x)=−3x2+8xf(x) = -3x^2 + 8x\newlineg(x)=2xg(x) = 2x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−3x2+8x)∗(2x)(f * g)(x) = (-3x^2 + 8x) * (2x)
  3. Perform multiplication: Distribute the terms of g(x)g(x) across the terms of f(x)f(x) to find the product.(f∗g)(x)=(−3x2∗2x)+(8x∗2x)(f * g)(x) = (-3x^2 * 2x) + (8x * 2x)(f∗g)(x)=−6x3+16x2(f * g)(x) = -6x^3 + 16x^2

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