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f ∈ F(A,B)
Your notation looks a bit weird to me. Is that exactly from a question? What normal notation would be:
Notice how you can go from A->B and then from B->C. But remember, that f and g are invertible, so you can go from B->A and from C->B. Use this, and show that if an element is in C, then the element must correspond to some element in A.
I need to prove the following: