combination of zsr zir functions

here is the question
https://i48.tinypic.com/23trpf5.jpg

i know that i should represent the signal as a series of step functions
and get zir/zsr combination of some sort


i know how to analize a circuit for zsr zir (zero state responce zero input response)
but i lack the theoretical knowledge of
dealing with a comlex sygnal like in the zir combination like here
?
is there some good reading i can do??