A man leaves his home early in the morning to have a walk. He arrives at a junction of roads A and B as shown in figure. He takes the following steps in later journies :

(i) 1 km in North direction.
(ii) Changes direction and moves in North-East direction for `2 sqrt(2)` km.
(iii) Changes direction and moves Southwards for distance of 2 km.
(iv) Finally he changes the direction and moves in South-East direction to reach road A again.
Visible/invisible path The path traced by the man in the direction parallel to road A and road B is called invisible path, the remaining path is called visible.
Visible points The point about which the man changes direction are called visible points, except the point from where he changes direction last time.
Now if roads A and B are taken as X-asix and Y-axis, then visible point representing the graph of y = f(x).
If f(x) is periodic with period 3, then f(19) is

Options

A. 2
B. 3
C. 19
D. None of these

Answer

A