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