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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x+6f(x) = -x + 6\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)=−x+6f(x) = -x + 6\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. Multiply Functions: We have:\newlinef(x)=−x+6f(x) = -x + 6\newlineg(x)=−4xg(x) = -4x\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x+6)∗(−4x)(f * g)(x) = (-x + 6) * (-4x)
  3. Distribute Terms: Distribute −4x-4x to both terms in the parentheses.\newline(f∗g)(x)=(−x∗−4x)+(6∗−4x)(f * g)(x) = (-x * -4x) + (6 * -4x)\newline(f∗g)(x)=4x2−24x(f * g)(x) = 4x^2 - 24x
  4. Simplify Polynomial: Express your answer as a simplified polynomial.\newlineThe polynomial 4x2−24x4x^2 - 24x is already in its simplest form.

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