In general case of deformed Heisenberg algebra leading to the minimal length, we present a definition of the inverse of position operator which is linear and two-sided. Our proposal is based on the functional analysis of the position operator. Using this definition, 1D Coulomb-like problem is studied. We find exactly the energy spectrum and the eigenfunctions for the 1D Coulomb-like potential in deformed space with arbitrary function of deformation. We analyze the energy spectrum for different partial cases of deformation function and find that the correction caused by the deformation highly depends on the type of the deformation function.
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