Solar gravity (g) modes propagate within the radiative part of the solar interior and are highly sensitive to the physical conditions of the solar core. They would represent the best tool to infer the structure and the dynamics of the radiative interior, in particular the core, if they were properly detected and characterized. Although individual rotational splittings for g modes have not yet been calculated, we have to understand the effect of these modes, and also low-degree high-frequency p modes, on the inversion of the solar rotation rate between 0.1 and 0.2R&sun;. In this work, we follow the methodology developed in Mathur et al. [2008, A&A, 484, 517] and García et al. [2008a, A.N., 329, 476], adding g modes and low-degree high-frequency p modes to artificial inversion data sets, in order to study how they convey information on the solar core rotation.