First slide

Functions (XII)

Question

$Period of f (x) = sgn ([x] + [- x]) is equal to (where [.] denotes greatest integer function)$

Moderate

A

1
B

2
C

3
D

does not exist

Solution

$[x] + [- x] = 0 i f x \in Z$
= $- 1 i f x \notin Z$
$N o w f (x) = S g n ([x] + [- x]) = S g n (0) = 0 i f x \in Z$
$= S g n (- 1) = - 1 i f x \notin Z$
$t h e r e f o r e f (x) p e r i o d i s 1$

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