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Also, let's say we have two functions ƒ, and g, with f:A→B and g:C→D. Let's say that the image of the function f is f(A) ⊆ C. That way, we made sure that gof is defined. So, do we write gof: A → D, that is, is the domain of gof A, and the codomain D, or is the codomain of gof the image of f(A), because gof: A→f(A)⊆C→g(f(A)), that is, it starts in A and ends up in g(f(A)).

Thank you.