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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=3xf(x) = 3x\newlineg(x)=−4x+3g(x) = -4x + 3\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)=3xf(x) = 3x\newlineg(x)=−4x+3g(x) = -4x + 3\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)=3xf(x) = 3x\newlineg(x)=−4x+3g(x) = -4x + 3\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(3x)∗(−4x+3)(f * g)(x) = (3x) * (-4x + 3)
  3. Distribute terms: Distribute 3x3x across the terms in g(x)g(x).
    (f∗g)(x)=3x∗(−4x)+3x∗3(f * g)(x) = 3x * (-4x) + 3x * 3
    (f∗g)(x)=−12x2+9x(f * g)(x) = -12x^2 + 9x

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