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f[f(x)]=1/[1 - 1/(1-x)]
=1/[(1-x)/(1-x) - 1/(1-x)]
=1/[(1-x-1)/(1-x)]
=1/[-x/(1-x)]=1/[x/(x-1)]
=(x-1)/x=1 - 1/x
则f{f[f(x)]}=1/[1 - (1 - 1/x)]
=1/(1 - 1 + 1/x)=1/(1/x)=x
=1/[(1-x)/(1-x) - 1/(1-x)]
=1/[(1-x-1)/(1-x)]
=1/[-x/(1-x)]=1/[x/(x-1)]
=(x-1)/x=1 - 1/x
则f{f[f(x)]}=1/[1 - (1 - 1/x)]
=1/(1 - 1 + 1/x)=1/(1/x)=x
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