Are there time where, instead of writing a function as $f(w,x,y,z)$ we would instead write it with more complicated arguments like $f(w,x,y-z,z)$?

Question

By "complicated arguments " I mean where the arguments are themselves functions (like $f(x,x^2,y,z)$ or something)

As a rough example, would we ever write $f(x,y)= (x-y)^2+x$ as $f(x-y,x)$ instead (can we even do this?)