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Question
If \[f\left( x \right) = \frac{x + 1}{x - 1}\] , show that f[f[(x)]] = x.
Solution
Given:
\[f\left( x \right) = \frac{x + 1}{x - 1}\]
Therefore,
\[f\left[ f\left\{ \left( x \right) \right\} \right] = f\left( \frac{x + 1}{x - 1} \right)\]
f [ f {(x)}] = x
Hence proved.
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