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

L.H.S :-

f(x) = 1 / 1 - x ....

So ... f[ f { f(x) } ]

= f [ f {1 / 1 - x } ]

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

= f [ (1 - x) / -x ]

= 1 / [1 - {(1 - x) / -x}] 

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

= 1 / {(x + 1 - x) / x}

= x / 1 = x = R.H.S ....

Proved ...

  • 19
surely you aren't actually that munted you spasticated flopper?
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