Short investigation into fruit served up for a piece of cake (2,7)
I believe the answer is:
no problem
'piece of cake' is the definition.
(I've seen this in another clue)
'short investigation into fruit served up' is the wordplay.
'short investigation' becomes 'prob' (I can't explain this - if you can you should give a lot more credence to this answer).
'into' indicates putting letters inside.
'fruit' becomes 'melon' (type of fruit).
'served up' is a reversal indicator (in a down clue, going upwards).
'melon' written backwards gives 'nolem'.
'prob' inserted into 'nolem' is 'NO PROBLEM'.
'for a' is the link.
Can you help me to learn more?
(Other definitions for no problem that I've seen before include "fine" , "Easy peasy!" , "of course" , "Don't worry about it!" .)