  The luminosity function of active galactic nuclei has been measured down to
luminosities ~10^{42} erg/s in the soft and hard X-rays. Some fraction of this
activity is associated with the accretion of the material liberated by the
tidal disruption of stars by massive black holes. We estimate the contribution
to the X-ray luminosity function from the tidal disruption process. While the
contribution depends on a number poorly known parameters, it appears that it
can account for the majority of X-ray selected AGN with soft or hard X-ray
luminosities <~10^{43}-10^{44} erg/s. If this is correct, a picture emerges in
which a significant portion of the X-ray luminosity function of AGN is
comprised of sources powered by tidal-disruption at the faint end, while the
sources at the bright end are powered by non-stellar accretion. Black holes
with masses <~2x10^6 Msun could have acquired most of their present mass by an
accretion of tidal debris. In view of the considerable theoretical uncertainty
concerning the detailed shape of the light curves of tidal disruption events,
we focus on power-law luminosity decay (as identified in candidate tidal
disruption events), but we also discuss constant accretion rate models.
