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Question
If f(x) = `((x + 1)/(x - 1))`, then prove that f(f(x)) = x.
Solution
f(x) = `((x + 1)/(x - 1))`
f(f(x)) = `((x + 1)/(x - 1) + 1)/(((x+1)/(x-1)) - 1)`
`= ((x + 1 + (x - 1)!)/(x-1))/(((x+1)-(x-1))/(x-1))`
`= (x+1+x-1)/(x+1-x+1)`
`(2x)/2` = x
Hence proved.
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