Backer briefly entering explosive function (7)
I believe the answer is:
tangent
'function' is the definition.
(tangent is a kind of function)
'backer briefly entering explosive' is the wordplay.
'backer' becomes 'angel' (an angel is a financial backer).
'briefly' means to remove the last letter.
'entering' means one lot of letters goes inside another.
'explosive' becomes 'tnt' (TNT is an example).
'angel' with its last letter taken away is 'ange'.
'ange' placed within 'tnt' is 'TANGENT'.
(Other definitions for tangent that I've seen before include "Straight line that touches but does not intersect a curve" , "At which one can go off" , "Straight line resting on a circle" , "Completely different line of thought - trigonometrical function" , "A new line of thought" .)