About an hour ago I answered this (now deleted) post:
https://math.stackexchange.com/questions/220018/showing-fx-is-constant
But after I answered (and there were a few comments) the OP posted a revised version (which I voted to close as an exact duplicate) and then deleted his original post (together with my answer and the comments).
The new post is very similar to the original question, and should of been an edit (and since the new question was edited I see the the OP does know how to edit).
What is the policy in this case ? can I see my answer ? (I would copy-paste it to the new post if I could)
Link to the new post: Showing $f(x)$ is constant.