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

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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]

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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)

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