Question

A man leaves his home early in the morning to have a walk. He arrives at a junction of road $A$ & road $B$ as shown in figure. He takes the following steps in later journey:
(a) $1 \,km$ in north direction
(b) changes direction & moves in north-east direction for $2 \sqrt{2} kms$.
(c) changes direction & moves southwards for distance of $2 \,km$.
(d) finally he changes the direction & 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 $A$ & road $B$ is called invisible path, the remaining path traced is visible.
Visible points :- The points about which the man changes direction are called visible points except the point from where he changes direction last time
Now if road $A$ & road $B$ are taken as $x$-axis & $y$-axis then visible path & visible point represents the graph of $y=f(x)$
If $f(x)$ is periodic with period 3 , then $f(19)$ is -

• A. 2
• B. 3
• C. 19
• D. none of these

Answer 1

Answer: (A)

$f(19)=f(3 \quad 6+1)=f(1)=2$