I have been challenged by my math teacher to solve this problem:
$f(x)=2x+[3x]$.
The inverse function is wanted.
I have tested several things, but no answer has also checked Geogebra.
2026-03-29 04:11:42.1774757502
inverse form of integer part function
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The function you consider is a piecewise linear function. You should probably study each piece separately.
For each integer $k \in \mathbb{Z}$, find the interval in which $\lfloor 3x \rfloor = k$, and the range of values of $f(x)$ for $x$ in that interval. On that range, $f(x) = 2x + k$, for which the inverse is straightforward to find.
Then if you want to have an explicit formula, find how to express $k$ using $f(x)$. Note that there might be several solutions!