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# If f ( x ) = 1 1 − x , show that f[f[f(x)]] = x. - CBSE (Science) Class 11 - Mathematics

#### Question

If  $f\left( x \right) = \frac{1}{1 - x}$ , show that f[f[f(x)]] = x.

#### Solution

Given

$f\left( x \right) = \frac{1}{1 - x}$

Thus,

$f\left\{ f\left( x \right) \right\} = f\left\{ \frac{1}{1 - x} \right\}$

$= \frac{1}{1 - \frac{1}{1 - x}}$

$= \frac{1}{\frac{1 - x - 1}{1 - x}}$
$= \frac{1 - x}{- x}$
$= \frac{x - 1}{x}$
Again ,
$f\left[ f\left\{ f\left( x \right) \right\} \right] = f\left[ \frac{x - 1}{x} \right]$
$= \frac{1}{1 - \left( \frac{x - 1}{x} \right)}$
$= \frac{1}{\frac{x - x + 1}{x}}$
$= \frac{x}{1}$
$= x$
Therefore,  f[f{f(x)}] = x.
Hence proved.
Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 3: Functions
Ex.3.20 | Q: 4 | Page no. 11
Solution If f ( x ) = 1 1 − x , show that f[f[f(x)]] = x. Concept: Functions.
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