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SomeRandomGuy

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Hey guys, wasn't sure what forum to post this in. So if this is the wrong forum, I apologize. Anyway, I have a problem in Real Analysis that I can't quite get. Here it is:

Let f:A->B and R is a relation on A such that xRy iff f(x) = f(y).

a.) Prove R is an equivalence relation

b.) Show g:A->E is surjective

c.) Show h:E->B is injective

d.) Prove f(x) = h(g(x)).

I solved parts a, b, and c. My problem is part d... I don't even know where to begin. It just doesn't make sense to me when I think about it. Thanks for any help.

EDIT: I just realized I didn't put what E is. E is the equivalence classes on any particular element. So, it's the set of all equivalence classes for this function.

Let f:A->B and R is a relation on A such that xRy iff f(x) = f(y).

a.) Prove R is an equivalence relation

b.) Show g:A->E is surjective

c.) Show h:E->B is injective

d.) Prove f(x) = h(g(x)).

I solved parts a, b, and c. My problem is part d... I don't even know where to begin. It just doesn't make sense to me when I think about it. Thanks for any help.

EDIT: I just realized I didn't put what E is. E is the equivalence classes on any particular element. So, it's the set of all equivalence classes for this function.

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