Let f : [-4, 4] ~ { − − π π , 0, π π } → → R, such that f(x…

Maths Functions, Limits, Continuity and Differentiability Functions Single Correct MCQ

Published on: August 13, 2026

Let f : [-4, 4] ~ { − − π π , 0, π π } → → R, such that f(x) = cot (sinx) + , where [.] denotes the greatest integer function, is an odd function. Complete set of values of 'a' is

(-16, 16) ~ {0}

(- ∞ ∞ , -16) ∪ ∪ (16, ∞ ∞ )

[-16, 16] ~ {0}

(- ∞ ∞ , -16) ∪ ∪ [16, ∞ ∞ )

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The correct answer is:

For f(x) to be odd, should not depend upon the value of x.

Since x ∈ ∈ [-4, 4] ⇒ ⇒ 0 ≤ x 2 ≤16

⇒ ⇒ = 0 if |a|> 16

⇒ ⇒ a ∈ ∈ (- ∞ ∞ , -16) ∪ ∪ (16, ∞ ∞ )

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