Need help to find inverse function $f(x)=x+\lfloor \frac x2\rfloor+\lfloor \frac x3\rfloor$

Question

I need to find inverse of below function$$f(x)=x+\lfloor \frac x2\rfloor+\lfloor \frac x3\rfloor$$ I saw its graph, it is an increasing function .
I can find inverse of $f(x)=x+\lfloor x\rfloor$ or $f(x)=x-\lfloor -x \rfloor$ but get stuck on this problem . Can someone give a hint or an idea !?

Thanks in advance.

This link is the graph of $f(x)$https://www.desmos.com/calculator/sxopqslw23 I find fractional part of $y$ is equal to fractional part of $x$ because $$y=x+\lfloor \frac x2\rfloor+\lfloor \frac x3\rfloor\\ \{y\}=\{x+\lfloor \frac x2\rfloor+\lfloor \frac x3\rfloor \}\\=\{x\}+\{\lfloor \frac x2\rfloor+\lfloor \frac x3\rfloor \}=\\\{x\}+0$$ but where can I go from here ?