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

Question

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

Satyajit Mohanty · Answer

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