FunctionHard
Question
Which of the following functions are aperiodic (where [.] denotes greatest integer function)
Options
A.y = [x + 1]
B.y = sin x2
C.y = sin2 x
D.y = sin-1 x
Solution
(A) f(x) = [x + 1] = [x] + 1 non periodic
(B) f(x) = sin x2 non periodic
(C) f(x) = sin2 x periodic with period π
(D) f(x) = sin-1 x monotonic ⇒ non-periodic
(B) f(x) = sin x2 non periodic
(C) f(x) = sin2 x periodic with period π
(D) f(x) = sin-1 x monotonic ⇒ non-periodic
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