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Without any further information, it probably means "apply the function $g$ to the number $x$, and return the complex conjugate of the (complex) number $g$ returns". But there is lots of opportunity for it to be defined as something different in a particular text. – Henning MakholmNov 20 '11 at 15:40
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Are you dealing with real or complex analysis? In complex analysis, $\overline{g(z)}$ is the complex congugate of $g(z)$. I am not aware of any universal meaning of $\overline{g(z)}$ in real analysis. – robjohn♦Nov 20 '11 at 15:41
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You saw this somewhere, did you not? Where did you see this? – J. M.Nov 20 '11 at 15:41