if the real valued function f(x)={(a)^x -1}/{(x^n)(a^x+1)} is even then n equals

f(x) = {a^x - 1}/{xⁿ(a^x + 1)}     ......................1

f(-x) = {a^-x - 1}/{(-x)ⁿ(a^-x + 1}

f(-x) = {1-a^x}/{xⁿ(1 + a^x)}(-1)ⁿ           

f(-x) = {-1/(-1)ⁿ} {f(x)}         ...................2 

f(x) is even function if f(x) = f(-x)

for this condition -1/(-1)ⁿ should be 1

n = 1 , 3 , 5 .........

n should be odd integer

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