Let's suppose product A performs a certain function and product b performs a second and different function. If these products are patented, could one patent a single product that performs both functions but is merely a combination of the two products?
It is possible that such a combination can be patented, and in fact it happens all of the time. However, there are basically two bars to hurdle with respect to patentability, and another bar even if a patent is granted.
The two bars to hurdle to try and get a patent on a combination are "obviousness" and "anticipation." "Obviousness" occurs when a combination is determined to be "obvious" to "one of ordinary skill in the art." So, even if your combination is not patented, and indeed maybe not even done, it can still be found to be an "obvious" improvement or combination, and therefore not entitled to a patent.
"Anticipation" exists when there is some sort of written documentation -- either another patent, or a paper, or even an advertisement -- that suggests or describes the combination or improvement in sufficient detail so that "one of ordinary skill in the art" could have created the combination or improvement themselves after reading the document. If a combination or improvement is "anticipated" it is also not entitled to a patent.
Generally, those are pretty big hurdles to overcome, especially when you are talking about a combination of existing products. As I noted in your other post, you really need to have some "unexpected" outcome in order to get a patent on a combination of existing products. There are some other ways around these barriers as well, but most are too detailed to really go into here.
Finally, even if you do get a patent on your combination or improvement, if the underlying "parts" of your invention are patented themselves, you may not be able to build, manufacture, assemble or sell your own invention -- or "practice" your invention -- without infringing on the underlying patents.
"If you have such an invention, you would be well-advised to sit down with a local patent agent or attorney (agent will be cheaper, generally) who can review your invention and advise you on the patentability of your invention.