Suppose $U,V\subset \mathbb{C}$ be two open sets. Let $g:U\to V$ be an analytic bijective function and $h:V\to \mathbb{R}$.
I know that if $h$ is harmonic, then $h\circ g$ is also harmonic. I'm trying to prove the converse: if $h\circ g$ is harmonic, then $h$ is harmonic.
However, I'm not entirely sure how to proceed. Any hint/help will be useful. Thanks in advance.