For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If th

Question

For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:

Accepted Answer

None of the above. Expression : f ( x + a ) = f ( a × x ) f (x + a) = f (a 	imes x) f ( x + a ) = f ( a × x ) Also, f ( 1 ) = 4 f(1) = 4 f ( 1 ) = 4 Now, f ( 1003 ) = f ( 1002 + 1 ) = f ( 1002 × 1 ) = f ( 1002 ) f(1003) = f(1002 + 1) = f(1002 	imes 1) = f(1002) f ( 1003 ) = f ( 1002 + 1 ) = f ( 1002 × 1 ) = f ( 1002