  Extragalactic sources from the IRAS Faint Source Catalog (FSC) which have the
optically faintest magnitudes (E > 18) were selected by spatial coincidence
with a source in the FIRST radio survey, and 28 of these sources have been
observed with the Infrared Spectrograph on Spitzer (IRS). While an infrared
source is always detected with the IRS at the FIRST position, only ~ 50% of the
infrared sources are real FSC detections, as estimated from the number of
sources for which the fv(25um) determined with the IRS is fainter than the
sensitivity limit for the FSC. Sources have 0.12 < z < 1.0 and luminosities
(ergs per s) 43.3 < log[vLv(5.5um)] < 46.7, encompassing the range from local
ULIRGs to the most luminous sources discovered by Spitzer at z ~ 2. Detectable
PAH features are found in 15 of the sources (54%), and measurable silicate
absorption is found in 19 sources (68%); both PAH emission and silicate
absorption are present in 11 sources. PAH luminosities are used to determine
the starburst fraction of bolometric luminosity, and model predictions for a
dusty torus are used to determine the AGN fraction of luminosity in all sources
based on log[vLv(5.5um)]. Approximately half of the sources have luminosity
dominated by an AGN and approximately half by a starburst. The ratio of
infrared to radio flux, defined as q = log[fv(25um)/fv(1.4 GHz)], does not
distinguish between AGN and starburst for these sources.
