'pepsin-inactive' is a compound of 'pepsin' and 'inactive'. 'pepsin' originates from Greek, specifically the word 'πέψις' (pepsis), where 'pepsis' meant 'digestion'. 'inactive' originates from Latin, specifically 'in-' (not) + 'activus' (active).

'pepsin' entered modern scientific English in the 19th century via German ('Pepsin') from Greek 'pepsis' (through modern Latin usage). 'inactive' developed from Latin 'inactivus' into Middle French/early modern English and became 'inactive' in modern English; the compound 'pepsin-inactive' is formed in modern scientific (biochemistry/physiology) usage by combining the enzyme name with the adjective.

Individually, 'pepsin' initially named the digestion-related enzyme, and 'inactive' meant 'not active'; combined in scientific contexts the phrase specifically denotes that a substance is not acted on (is resistant or inactive) by pepsin. The compound meaning is a technical specialization rather than a semantic shift of the individual roots.