We investigate the far-infrared (FIR) properties of X-ray sources detected in the Chandra Deep Field-South (CDF-S) survey using the ultradeep 70 and 24 μm Spitzer observations taken in this field. Since only 30 (i.e. ≈ 10 per cent) of the 266 X-ray sources in the region of the 70 μm observations are detected at 70 μm, we rely on stacking analyses of the 70 μm data to characterize the average 70 μm properties of the X-ray sources as a function of redshift, X-ray luminosity and X-ray absorption. Using Spitzer-IRS data of the Swift-Burst Alert Telescope (BAT) sample of z ≈ 0 active galactic nuclei (AGNs), we show that the 70/24 μm flux ratio can distinguish between AGN-dominated and starburst-dominated systems out to z ≈ 1.5 . Among the X-ray sources detected at 70 μm, we note a large scatter in the observed 70/24 μm flux ratios, spanning almost a factor of 10 at similar redshifts, irrespective of object classification, suggesting a range of AGN:starburst ratios. From stacking analyses we find that the average observed 70/24 μm flux ratios of AGNs out to an average redshift of 1.5 are similar to z ≈ 0 AGNs with similar X-ray luminosities (L_X = 10^(42-44) erg s^(−1)) and absorbing column densities (N_H ≤ 10^(23) cm^(−2)) . Furthermore, both high-redshift and z ≈ 0 AGNs follow the same tendency towards warmer 70/24 μm colours with increasing X-ray luminosity (LX). From analyses of the Swift-BAT sample of z ≈ 0 AGNs, we note that the 70 μm flux can be used to determine the IR (8–1000 μm) luminosities of high-redshift AGNs. We use this information to show that L_X = 10^(42-43) erg s^(−1) AGNs at high redshifts (z = 1–2) have IR to X-ray luminosity ratios (L_(IR)/L_X) that are, on average, 4.7^(+10.2)_(−2.0) and 12.7+7.1−2.6 times higher than AGNs with similar X-ray luminosities at z = 0.5–1 and ≈0, respectively. By comparison, we find that the L_(IR)/L_X ratios of L_X= 10^(43-44) erg s^(−1) AGNs remain largely unchanged across this same redshift interval. We explore the consequences that these results may have on the identification of distant, potentially Compton-thick AGNs using L_(IR)/L_X ratios. In addition, we discuss possible scenarios for the observed increase in the L_(IR)/L_X ratio with redshift, including changes in the dust covering factor of AGNs and/or the star formation rates of their host galaxies. Finally, we show how deep observations to be undertaken by the Herschel Space Observatory will enable us to discriminate between these proposed scenarios and also identify Compton-thick AGNs at high redshifts
