This challenging limits use operations and compositions of graphically and algebraically defined functions. This circuit is difficult. It is best for teachers to polish their skills on this style of problems and possibly to grab a couple of ideas for exam problems.
If you put it in front of students, use it with very strong students or consider pairing or tripling up to do as a team activity.
Circuit includes graphs of the resulting relationships and a link to Desmos graphs with points to drag to help illustrate results.