The repulsive a (3)Sigma (+)(u) state potential of the Na-2 molecule is determined by applying the IPA (inverse perturbation approach) of V. S. Ivanov and V. B. Sovkov [Chem. Phys. 213, 295 (1996)] to the analysis of the Na-2 2 (2)Sigma (+)(g) (v=15, N=27, and v=5, N=39)-->a (3)Sigma (+)(u) continua observed in the work of T. J. Whang [J. Mol. Spectrosc. 160, 411 (1993)]. The resulting a (3)Sigma (+)(u) state potential is close to the ab initio potential within the experimental error, but its right branch deviates from the RKR-Le Roy-Bernstein potential function of the a (3)Sigma (+)(u) state shallow well reported in E.-J. Friedman-Hill and R. W. Field [J. Chem. Phys. 96, 2444 (1992)]. The transition moment function M(R) of the 2 (3)Sigma (+)(g)-a (3)Sigma (+)(u) transition is also obtained from the analysis of the spectra and compared to the ab initio one. The same 2 (3)Sigma (+)(g) (v=15, N=27)-->a (3)Sigma (+)(u) experimental spectrum is used for investigating abilities of the WKB nodes method, the FCF phase method, and the method of the accurate equation for the potential in terms of the transition amplitudes. They were developed earlier by us in order to determine the bound state potential function from the structure of the bound-free continuous spectrum alone without using information about the ro-vibrational term values. This attempt resulted in very reliable potential curves.