Inverse function for $y=\lfloor x\rfloor+x$

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Find the inverse function of the following function:

$y=\lfloor x\rfloor +x$

I have tried writing down $x$ as $\lfloor x\rfloor +\{x\}$ but didn't get anywhere with that.

A proper hint would be highly appreciated. Thanks

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Hint: If $y = \lfloor x \rfloor + x$, then what can we say about the fractional parts of $x$ and $y$?