The following are taken from the 新明解国語辞書.
取り [接頭語的に] 動詞に冠し、「十分に、慎重に、確実に」などの意を加える。「ーあつかう・ーつくろう・ー調べる」
and there are more examples like this. However, the corresponding verbs 「取る」「打つ」 do not seem to have these meanings, nor do the kanjis (as I understand it from a native Chinese speaker's perspective).
So my question is, how do these stem forms acquire these meanings?
To elaborate, is it related to the history (classical Japanese perhaps) or how Japanese people understand these things? Do native Japanese consider 取る+調べる to naturally have the meaning of 取り調べる, or is the 取り in 取り調べる understood as "something different" as well by native speakers? How to make the difference more easy to understand for Japanese learners?
Personally I found it very confusing when I attempted to get the meaning of 取り調べる from 取る+調べる (or 取って調べる). A even worse case is attempting to get the meaning of 打ち明ける from 打って明ける which does not seem to be used at all in Japanese according to Google. It didn't seem clear to me until I saw the quotes above and learnt that they can mean something different.