difficult function help?

Let f : X → Y and g : Y → Z be functions.

(i) Write down the denition of the image of f and the composition g ∘ f.

(ii) What constraint must be imposed on X and the image of g in order for f ∘ g

to also be well-dened? State the domain and co-domain of f ∘ g.

need help answering part two please show all details

in case im wrong here is what i believe part one to be

i believe the answer to part one is that the image of f is the set of value {f(x)|x∈X} i.e all the values that f(x) can take given the domain X.

and that the composition function is g ∘ f : X → Z such that g ∘ f(x)=g(f(x))