The answer is B, [tex]-|x|[/tex].
Here's analyses of the other options:
Option A. You can clearly see that [tex] \frac{1}{|x|} [/tex] is not defined for [tex]x=0[/tex], so the function [tex] \frac{1}{|x|} [/tex] doesn't have the same domain as that of [tex]|x|[/tex], hence can't be the answer.
Option C. By the definition of absolute value, we know that [tex]|-x|=|x|[/tex], this is the same function, hence not the answer.
Option D. This is just [tex]|x|[/tex] shifted one unit to the right, not flipped.
