Question

Which of the following functions is not periodic, where [ . ] denotes greatest integer function 

(A) f(x) = 1^[x] + (–1)^[x] 

(B) g(x) = 1^[5x] + (–1)^[5x] 

(C) h(x) = 2^[x] – (–2)^[x] 

(D) ϕ(x) = 1^[x] – (–1)^[x]

Answer 1

Correct Option:-  (C) h(x) = 2^[x] – (–2)^[x]

Explanation :-

(A) f(x + T) = 1^{[x + T]} + (– 1)^{[x + T]} = 1^[x] + T + (– 1)^[x] + T 

Periodic for T is even 

Similarly for B and D 

(C) h(x + T) = 2^{[x] + T} – (– 2)^{[x] + T} = 2T (2^[x] – (– 2)^[x] (– 1)T ) ≠ h(x)