CBSE (Science) Class 11CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Login
Create free account


      Forgot password?

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.
S
View in app×