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Given $f(f(x))=x+2$ does it necessarily follow that $f(x)=x+1$? This question comes from a precalculus algebra student.

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    Are you working with functions from $\mathbb R$ to $\mathbb R$? From $\mathbb Z$ to $\mathbb Z$?2012-11-06
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    I am very impressed by the ingenuity of the answers. Many thanks. Perhaps I should add that the question was raised by a student of mine.2012-11-06

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