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Question
Determine whether the following function is odd or even?
f(x) = `((a^x - 1)/(a^x + 1))`
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Solution
f(-x) = `((a^-x - 1)/(a^-x + 1))`
`= ((1/a^x - 1)/(1/a^x + 1))`
`= (1 - a^x)/(1 + a^x)`
`= - ((a^x - 1)/(a^x + 1))`
Thus f(-x) = - f(x)
∴ f(x) is an odd function.
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