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The room-temperature optical pseudo-dielectric-functions of single-phase, single-crystalline rocksalt-structure MgxZn1-xO with Mg-content x between 0.68 and 1 were determined in the photon energy range from 0.75 to 9.10 eV using spectroscopic ellipsometry. The refractive index determined in the spectral region below the fundamental absorption edge decreases with increasing Mg content. The pseudo-dielectric-functions reveal structures caused in critical points due to electronic band-to-band transitions and free exciton formation at the fundamental band-gap transition. Standard model dielectric function approaches were applied for line shape analysis. Upon increase of the bond ionicity with increasing Mg content the energies of the band-to-band transitions as well as the fundamental-band-gap exciton binding energy parameters increase, while the Γ-point spin-orbit-splitting energy parameter decreases. We compare our results with the band-gap properties of wurtzite-structure MgxZn1-xO with Mg-content x between 0 and 0.5 obtained previously, and we discuss discontinuities across the phase transition. We provide estimates for the band gap bowing parameter of rocksalt-structure MgxZn1-xO and the band-gap value of rocksalt-structure ZnO.