Change of Determinant of Metric Under Var Change

[ChrisVer]

Under a change of variables:
$x^{\mu} \rightarrow x^{\mu}+ \delta x^{\mu}$

How can I see how the determinant of the metric changes?
$\sqrt{|g(x)|}$?

Is it correct to see it as a function?
$f(x) \rightarrow f(x+ \delta x) = f(x) + \delta x^{\mu} \partial_{\mu} f(x)$
?

 

[Matterwave]

It seems like you're trying to find the variation of the determinant? You might look here: http://en.wikipedia.org/wiki/Hilbert_action#Variation_of_the_determinant