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$f$ is analytic in {$z:|z|>1$} and $f(r)\in\mathbb R$ $\forall$ real $r>1$. How can I show that the same hold $\forall$ real $r<-1$?

Please don't solve it completely. I'm just looking for a clue. Thanks.

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    @froggie You could post your comment as an answer (hence I will upvote).2013-04-22

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