# Proving the behavior of a function on symmetric domain

This is a problem I am stuck at. I think this problem has to do with Riemann mapping theorem and Schwarz reflection principle, but I cannot find a way to solve it... Could anyone please help me how to solve this problem?

• Look at $g \colon z \mapsto \overline{f(\overline{z})}$. What do you know about $g$? – Daniel Fischer Oct 9 '17 at 11:08
• All I can see is that $g$ is another analytic function. Could you tell me what I am missing? – Keith Oct 9 '17 at 12:01
• See this question and this one. – Daniel Fischer Oct 9 '17 at 12:11