I need help understanding the notation of a question regarding 2 functions

Question

In my homework, there were 2 functions defined as such:

f((x,y))=x-y , f:ℕ^2→ℤ

g((x,y))=(x-y,x+y) , g:ℕ^2→ℕ^2

I was asked to prove whether the functions are injective, surjective and find their Image, which I did. But in the next section, I was asked to find "f ∘ g" and "g ∘ g", and I have no clue what this notation means because the teacher never used it during the lessons. Does it mean something about the domain and codomain of the functions?

Answer 1

I found out what ∘ means: it's a composition of 2 functions.

For example, f∘g of the functions f(x)=x^2 f:A → B and g(y)=y+1 f:B → C

f(g(y)) = f(y+1) = (y+1)^2 f: A → C