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f: [− 4, 4] ∼ {−π, 0, π} → R, when f(x) = cot(sinx) + [ x2/a] , when [·] denotes the greatest integer function. If f be an odd function, then the set of values of a is

(A)  (−16, 16) ∼ {0}

(B)  (−∞, −16) ∪ (16, ∞)

(C)  [−16, −16] ∼ {0}

(D)  (−∞, −16] ∪ [16, ∞)

1 Answer

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Best answer

Correct option  (B)  (−∞, −16) ∪ (16, ∞)

Explanation :

For f(x) to be odd, then [ x2/a|] should depend upon the value of x.

x ∈ [−4, 4] ⇒ 0 ≤ x2 ≤ 16

 Now, [x2/a|]  = 0 if

|a| > 16 ⇒ a ∈ (−∞, −16)∪(16, ∞)

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