What does the "~ておく" mean in "任せておく"?

Question

Good afternoon all,

From what I understand, "~ておく" basically has 4 meanings:

1. to do something for a purpose / reason

2. used as a softener (source)

3. to do.. for now or for the time being (source, source), in other words to leave a situation as it is for now or for some time (source)

4. used as a request / command (source)

I was wondering which of the above meaning is the implied meaning of "~ておく" when we use the word "任せておく" in the sentence "任せておけ！" ?

Is it the first meaning: "Leave it to me! (and your reason being that I will get the job done for you)",

Or is it the third meaning: "(For the time being,) Leave it to me!" ?

PS: Btw just to confirm, is it true that the "~ておく" of "放っておく" implies the third meaning?

Answer 1

I'll just leave my comment above as an answer to maybe be ticked off since people seem to agree with it:

I was taught that ~ておく means "to do something in preparation (for something else)", (ie. nr.1 there) but I'm sure there's many (probably similar) applications..

As sawa also points out in his comment, your point 2 and 4 doesn't seem to make much sense, and point 3 is also a bit fuzzy.

Furthermore, as a side note, ~ておく at least in speech is often shortened to ~とく, as also noted in this question.

Answer 2

I was taught ～ておく means "to leave something all set". In fact I've seen it written with ～て置く.