If function f satisfies the relation f ( x ) ⋅ f ′ ( − x ) = f ( − x ) ⋅ f ′ ( x ) for all x and f ( 0 ) = 3 , now if f ( 3 ) = 3 , then the value of f ( − 3 ) is

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f ( x ) × f ′ ( − x ) = f ( − x ) × f ′ ( x ) ​ ⇒ f ′ ( x ) × f ( − x ) − f ( x ) × f ′ ( − x ) = 0 ​ ⇒ d x d ​ [ f ( x ) f ( − x )] = 0 ​ ⇒ f ( x ) f ( − x ) = k ​ Give ( f ( 0 ) ) 2 = k = 9 ⇒ k = 9 ​ Then f ( 3 ) f ( − 3 ) = 9 ⇒ f ( − 3 ) = 3 ​

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