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Question
If f(x) = `(x - 1)/(x + 1)`, then show that `f(1/x)` = – f(x)
Solution
f(x) = `(x - 1)/(x + 1)`
Substituting x by `1/x`, we get
`f(1/x) = (1/x - 1)/(1/x + 1)`
= `((1 - x)/x)/((1 + x)/x)`
= `(1 - x)/(1 + x)`
= `(-(x - 1))/(1 + x)`
= `- (x - 1)/(x + 1)`
Therefore,
We get `f(1/x)` = – f(x)
Hence proved.
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