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The recent generalizations of the Boltzmann–Gibbs statistics mathematically relyon the deformed logarithmic and exponential functions defined through some deformation parameters. In the present work, we investigate whether a deformedlogarithmic/exponential map is a bijection from R+ /R  set of positive real numbers/all real numbers  to R/R+, as their undeformed counterparts. We show that theirinverse map exists only in some subsets of the aforementioned  co domains. Furthermore, we present conditions which a generalized deformed function has tosatisfy, so that the most important properties of the ordinary functions are preserved.The fulfillment of these conditions permits us to determine the validityinterval of the deformation parameters. We finally apply our analysis to Tsallisq-deformed functions and discuss the interval of concavity of the Rényi entrop

A note on the definition of deformed exponential and logarithm functions