Question

if f(x)=1/1-x then prove that f[f{f(x)}]=x​

Answer 1

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 ...

Hope it's Helpful for you...

Answer 2

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

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

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

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

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

Hence LHS = RHS proved