Find the domain of the function,

$\log x$ function has domain $R^{+}$.

When x is replaced by |x|, the function f shows value as

$f(x)=\log (x) ; x>0$

$=\log (-x) ; x<0$

Hence in the function x cannot be zero as log function is not defined for x=0.

Domain of f(x) is R – {0}