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if the real - valued function f(x)= ax-1/xn(ax+1) is even then n equals

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Please find below the solution to the asked query :

fx=ax-1xn ax+1f-x=a-x-1-xn a-x+1=1ax-1-xn 1ax+1=1-axax-xn 1+axax=-ax-1-xn ax+1For even function fx=f-xSo , it will be equal when n is odd .
 
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View Full Answer
If this function is even , f ( x ) + f ( - x ) = 0 is absolutely true
f ( - x ) =   ( a - x - 1 ) / { (- x ) n ( a - x + 1 ) } = f ( x ) =   ( a x - 1 ) / { ( x ) n ( a x + 1 ) } 
=> comparing them yields that n must be an odd number for the condition f ( x ) + f ( - x ) = 0 to be satisfied
Hence , n may be any odd number like 1 , 3 , 5 ...
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