If f is real function satisfying the relation f ( x + y ) = f ( x ) . f ( y ) for all x , y ∈ R and f ( A ) = 2 and a ∈ N , for which ∑ K = 1 n f ( a + k ) = 16 ( 2 n − 1 ) then a = ____

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If f is real function satisfying the relation f ( x + y ) = f ( x ) . f ( y ) for all x , y ∈ R and f ( A ) = 2 and a ∈ N , for which ∑ K = 1 n ​ f ( a + k ) = 16 ( 2 n − 1 ) then a = ____

TestHub · Accepted Answer

​ f ( a ) = a n ; ​ ∑ f ( a + K ) = ∑ f ( a ) f ( K ) ​ = 2 a K = 1 ∑ n ​ 2 K = 2 a ( 2 n − 1 ) ​ ​ ∴ a = 3 ​

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