composition of functions

When I was in grade 9 English class, it was in the same room of the senior math teacher.  I remember seeing on the board the title "The Washer and Dryer Theory".  This is what the teacher (Mrs P) called it.  I remember a few years later when I had her for math and she taught us this "composition of  functions" that I was so disappointed.  Dry dirty clothes are the input into the washing machine.  Wet clean clothes are the output from the washing machine which become the input into the dryer.  The output of the dryer are the dry clean clothes.  Ugh.   Oh well.  I saw this on twitter and thought it was perfect.

Oh by the way the solution to the problem from Friday is 2.  Why?  I will tell you tomorrow.