  The cosmic far infrared background detected recently by the COBE-DIRBE team
is presumably due, in large part, to the far infrared (FIR) emission from all
galaxies. We take the well-established correlation between FIR and radio
luminosity for individual galaxies and apply it to the FIR background. We find
that these sources make up about half of the extragalactic radio background,
the other half being due to AGN. This is in agreement with other radio
observations, which leads us to conclude that the FIR-radio correlation holds
well for the very faint sources making up the FIR background, and that the FIR
background is indeed due to star-formation activity (not AGN or other possible
sources). If these star-forming galaxies have a radio spectral index between
0.4 and 0.8, and make up 40 to 60% of the extragalactic radio background, we
find that they have redshifts between roughly 1 and 2, in agreement with recent
estimates by Madau et al. of the redshift of peak star-formation activity. We
compare the observed extragalactic radio background to the integral over the
logN-logS curve for star-forming radio sources, and find that the slope of the
curve must change significantly below about 1 microjansky. At 1 microjansky,
the faint radio source counts predict about 25 sources per square arcminute,
and these will cause SIRTF to be confusion limited at 160micron.
