First slide

Functions (XII)

Question

$If f (x + 2 a) = f (x - 2 a), then f (x) is$

Moderate

A

a periodic function with period 4a
B

a periodic function with period 2a
C

a periodic function with indeterminate period
D

a non periodic function

Solution

$g i v e n e q u a t i o n i s f (x + 2 a) = f (x - 2 a)$
$r e p l a c e x b y x + 2 a$
$t h e n t h e g i v e n e q u a t i o n b e c o m e s f (x + 4 a) = f (x) \Rightarrow f (x) i s p e r i o d i c f u n c t i o n w i t h p e r i o d = 4 a$

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