word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."
In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
late 14c., "making, producing immediate effect, active, effective," from Old French efficient and directly from Latin efficientem (nominative efficiens) "effective, efficient, producing, active," present participle of efficere "work out, accomplish," from assimilated form of ex "out" (see ex-) + facere "to do" (from PIE root *dhe- "to set, put"). Meaning "productive, skilled" is from 1787. Related: Efficiently.
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Harper, D. (n.d.). Etymology of inefficient. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/inefficient