Middle English foode, fode, from Old English foda "food, nourishment; fuel," also figurative, from Proto-Germanic *fodon (source also of Swedish föda, Danish föde, Gothic fodeins), from Germanic *fod- "food," from PIE *pat-, extended form of root *pa- "to feed."
Food chain is by 1915. Food poisoning attested by 1864; food processor in the kitchen appliance sense from 1973; food stamp (n.) is from 1962.
It forms all or part of: antipasto; appanage; bannock; bezoar; companion; company; feed; fodder; food; forage; foray; foster; fur; furrier; impanate; pabulum; panatela; panic (n.2) "type of grass;" pannier; panocha; pantry; pastern; pastor; pasture; pester; repast; satrap.
It is the hypothetical source of/evidence for its existence is provided by: Greek pateisthai "to feed;" Latin pabulum "food, fodder," panis "bread," pasci "to feed," pascare "to graze, pasture, feed," pastor "shepherd," literally "feeder;" Avestan pitu- "food;" Old Church Slavonic pasti "feed cattle, pasture;" Russian pishcha "food;" Old English foda, Gothic fodeins "food, nourishment."