I am contemplating on combining the signals from two antennas onto one
cable using some sort of an "RF combiner" (is this the right term? Is
"RF mixer" a better term?).

The idea is that I combine the signal from a dedicated omnidirectional
FM antenna and a dedicated omnidirectional VFH/UFH antenna, since I
have only one cable run in the house and I want to use it for both FM
and TV reception.

Does this idea make sense at all?

If so, what's the market name of this "RF combiner" device I should be
shopping for? Can you recommend a specific one? (does Radio-Shack have
such?)

Thanks,
Daniel