3. The equation ||$x|-1|=a$ has exactly three real solutions. Then $a$ equals ( ).
(A) 0
(B) 0.5
(C) 1
(D) $\sqrt{2}$
3.C.

Graphical method: Draw the graph of the function $y=|| x | -11$ (as shown in Figure 5). When a line parallel to the $O x$ axis, $y=a$, intersects the graph of the function $y=|| x|-1|$ at exactly three points, $a=1$.