"liable to be held responsible," 1540s, from answer (v.) in the "be responsible for" sense + -able. The less-common meaning "able to be answered" is from 1690s.
Entries linking to answerable
answer v.
Middle English answeren, from Old English answarian "make a statement in reply," from and- "against" (from PIE root *ant- "front, forehead," with derivatives meaning "in front of, before") + swerian "to swear" (see swear), suggesting an original sense of "make a sworn statement rebutting a charge."
The meanings "conform, correspond" and "be responsible for" are from early 13c; that of "suffer the consequences of" is from late 13c.; that of "respond in antiphony" is from early 15c. The sense of "respond in act or action, give back in kind" is from 1570s; that of "solve, find the result of" is from 1742. Related: Answered; answering. The telephone answering machine was so called by 1961.
-able
common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).
A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."
To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]
In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.
unanswerable adj.
1610s, "admitting of no answer," from un- (1) "not" + answerable.