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For questions requesting examples of a certain structure or phenomenon

2 votes
2 answers
2k views

Example of a function that behaves like another function

I need a function $f(x)$ with the following properties - It should be monotonically non-decreasing. For $x \geq 1$, $x + \frac{1}{x} - f(x) < \epsilon$ where $\epsilon$ is an extremely small positiv …