If f : [ − 4 , 4 ] − { − π , o , π } → R , such that f ( x ) = cot ( sin x ) + [ ∣ a ∣ x 2 ] + x 2 s i n 2 x , ([.] denotes greatest integer function) is an odd function, then the complete set of

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If f : [ − 4 , 4 ] − { − π , o , π } → R , such that f ( x ) = cot ( sin x ) + [ ∣ a ∣ x 2 ​ ] + x 2 s i n 2 x ​ , ([.] denotes greatest integer function) is an odd function, then the complete set of values of ' a ', is

TestHub · Accepted Answer

For f ( x ) to be odd, [ ∣ a ∣ x 2 ​ ] should not depend on value of x. Since x ∈ [ − 4 , 4 ] ⇒ 0 ≤ x 2 ≤ 16 ⇒ [ ∣ a ∣ x 2 ​ ] = 0 if ∣ a ∣ > 16 ⇒ a ∈ ( − ∞ , − 16 ) ∪ ( 16 , ∞ )

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