If f(x)=1 1-x , then f(f(f(x))) is - Vidyadip

MCQ

If $f(x)=\frac{1}{1-x}$, then $f(f(f(x)))$ is

A
$x-1$
B
$1-x$
✓
$x$
D
$-x$

✓

Answer

Correct option: C.

$x$

(C) $\mathrm{x}$
Hint:
$f(x)=\frac{1}{1-x}$
$f(f(x))=f\left(\frac{1}{1-x}\right)=\frac{1}{1-\left(\frac{1}{1-x}\right)}$
$=\frac{1-x}{1-x-1}=\frac{x-1}{x}$
$f(f(f(x)))=f\left(\frac{x-1}{x}\right)=\frac{1}{1-\left(\frac{x-1}{x}\right)}=\frac{x}{x-x+1}=x $

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