Inverse $f^ {-1}$ of floor function

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How to solve: Let $f: R \to R$ be defined by $f(x)=\lfloor x \rfloor$. Find $f^{-1}(B)$ for B={0,1}?

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$f^{-1}$ here does not stand fo the inverse function, which obviously does not exist. It stands for the pre-image of the set $B$. The real numbers $x$ with floor equal to zero or one are those in the interval $[0,2)$