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66. \( f(x)=\frac{x^{2}-x+5}{x} \)

Ask by Bolton Stanley. in the United States
Feb 25,2025

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\( f(x) = x - 1 + \frac{5}{x} \)

Solución

Calculate or simplify the expression \( (x^2-x+5)/x \). Divide the polynomials by following steps: - step0: Using Long Division to Divide Polynomials: \(\frac{\left(x^{2}-x+5\right)}{x}\) - step1: Calculate: \(x-1+\frac{5}{x}\) The simplified form of the function \( f(x) = \frac{x^{2}-x+5}{x} \) is \( f(x) = x - 1 + \frac{5}{x} \).

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The function \( f(x) = \frac{x^{2} - x + 5}{x} \) can be rewritten to show its components more clearly. By simplifying, you can express it as \( f(x) = x - 1 + \frac{5}{x} \). This form makes it easier to analyze its behavior, such as identifying asymptotes and examining limits as \( x \) approaches zero. In real-world applications, rational functions like this one can model various scenarios, such as rates of change, population growth, or resource consumption. For instance, if you consider \( f(x) \) to represent costs over time, understanding how the function changes can help with budgeting strategies or planning investments based on how \( x \) (time or quantity) influences overall costs.

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