Don't think of the domain as one big function. Think of it as 3 parts as in the descrption:

C1: line from (0,0) to (1,0)

C2: circular arc from (1,0) to the line x=y. What is x in this case?

C3: line from (x,x) to (0,0)

If you don't know how to parametrize lines, look in your book somewhere around parametric equations of a line.

The circular arc you can just parametrize using sines and cosines.

I hope this helps!