An appropriate solution depends critically on the meanings of the \overline and ' ("prime") operations. Do please let us know what these operations mean.

If "prime" denotes transposition -- say, of a matrix or vector -- I think you should write either

f(x',\overline{x}')

or, better yet,

f(x',\bar{x}')

A happy side effect of making this change is that you needn't worry about the placement of the "prime" symbol.

But, again, absent knowledge of the meanings of the two operations, it's not possible to provide definitive formatting advice.

\documentclass{article}
\begin{document}
\[ 
f(x',\overline{x'}) \quad f(x',\overline{x}') \quad f(x',\bar{x}')
\]
\end{document}