ABSTRACT We model the X-ray surface brightness distribution of emission associated with Fanaroff & Riley type-II radio galaxies. Our approach builds on the RAiSE dynamical model which describes broad-band radio frequency synchrotron evolution of jet-inflated lobes in a wide range of environments. The X-ray version of the model presented here includes: (1) inverse-Compton upscattering of cosmic microwave background radiation; (2) the dynamics of the shocked gas shell and associated bremsstrahlung radiation; and (3) emission from the surrounding ambient medium. We construct X-ray surface brightness maps for a mock catalogue of extended FR-IIs based on the technical characteristics of the eRosita telescope. The integrated X-ray luminosity function at low redshifts (z ≤ 1) is found to strongly correlate with the density of the ambient medium in all but the most energetic sources, whilst at high-redshift (z > 1) the majority of objects are dominated by inverse-Compton lobe emission due to the stronger cosmic microwave background radiation. By inspecting our mock spatial brightness distributions, we conclude that any extended X-ray detection can be attributed to AGN activity at redshifts z ≥ 1. We compare the expected detection rates of active and remnant high-redshift radio AGNs for eRosita and LOFAR, and future more sensitive surveys. We find that a factor of ten more remnants can be detected using X-ray wavelengths over radio frequencies at z > 2.2, increasing to a factor of 100 for redshifts z > 3.1.