Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
brain-fag is a noun meaning "exhaustion that affects mental keenness". It carries one recorded sense.
exhaustion that affects mental keenness
Definitions, synonyms and semantic relations for brain-fag come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.