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How can I find $x$ having integer $f(x)$?

For example, when there are $f(x) = 5e^{-x}$ or $f(x) = -x + 6$ etc..., I want to find all x having integer $f(x)$.

How can I find it? It doesn't matter if it's another function.

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    If you can get the function inverse, you could write $f(x)=n=5e^{-x}$, then the values are $x_n = - \log(n/5)$, for all the possible values of $n \in \mathbb{Z}$. This might run into problems for other functions, and certain values of $n$. – Benedict W. J. Irwin Aug 14 '19 at 18:25
  • It's impossible really to do this for all functions. – kingW3 Aug 14 '19 at 18:44

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