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If `f(x)=1/(1-x)` , show that`f[f{f(x)}]=xdot`

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If `f(x)=1/(1-x)` , show that`f[f{f(x)}]=xdot`
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`f(x)=(1)/((1-x))impliesf{f(x)}=(1)/({1-(1)/((1-x))})=(1-x)/(-x) " "["replace x by "(1)/((1-x))]`
`impliesf[f{f(x)}]=({(1)/((1-x))-1})/((1)/((1-x)))=(x)/(1-x)xx((1-x))/(1)=x`.
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