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What is (f−g)(x)(f - g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=3x2−3g(x) = 3x^2 - 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)=−x2f(x) = -x^2\newlineg(x)=3x2−3g(x) = 3x^2 - 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 difference 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. Substitute Functions: Substitute the given functions into the formula.\newlineWe have:\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=3x2−3g(x) = 3x^2 - 3\newlineNow, calculate (f−g)(x)(f - g)(x) using the given functions.\newline(f−g)(x)=f(x)−g(x)(f - g)(x) = f(x) - g(x)\newline(f−g)(x)=(−x2)−(3x2−3)(f - g)(x) = (-x^2) - (3x^2 - 3)
  3. Calculate (f−g)(x)(f - g)(x): Simplify the expression by distributing the negative sign and combining like terms.\newline(f−g)(x)=−x2−3x2+3(f - g)(x) = -x^2 - 3x^2 + 3\newline(f−g)(x)=−4x2+3(f - g)(x) = -4x^2 + 3

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