Question

Let f : [-4, 4] ~ {−π, 0, π} →R, such that f(x) = cot (sinx) + $\left\lbrack \frac{x^{2}}{a} \right\rbrack$, where [.] denotes the greatest integer function, is an odd function. Complete set of values of 'a' is

• A. (-16, 16) ~ {0}
• B. (-∞, -16) ∪ (16, ∞)
• C. [-16, 16] ~ {0}
• D. (-∞, -16) ∪ [16, ∞)

Answer 1

Answer: (B)

(-∞, -16) ∪ (16, ∞)

Answer 2

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

Since x ∈ [-4, 4] ⇒ 0 ≤ x² ≤16

⇒ $\left[ \frac { x ^ { 2 } } { | a | } \right]$ = 0 if |a|> 16

⇒ a ∈ (-∞, -16) ∪ (16, ∞)