Which of the following functions are not periodic (where [ . ] denotes greatest integer function) :
(i) f(x) = sin 
(ii) f(x) = x + sin x
(iii) f(x) = [sin 3x] + |cos 6x|
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i) Let f(x) = sin 
is a periodic function with period T (a positive constant)
∴ f (x + T) = f(x) ⇒ sin 
= sin 
⇒ 
= n π + (–1) n 
, n ∈ I
since for no value of n, T is indepedent of x which contradicts that sin 
is a periodic function. Hence it is a non periodic function.
(ii) Let f(x) = x + sin x is a periodic function with period T.
x + T + sin (x + T) = x + sin x ⇒ T + sin (x + T) = sin x ⇒ T + 2 cos 
= 0
There is no positive constant value of T for which this equation holds true so f(x) is non- periodic function.
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