Limits Continuity And Differentiability Question 120
Question: If $ f(x)=\frac{1}{1-x} $ , then the points of discontinuity of the function $ f[f{f(x)}] $ are
Options:
A) {0, -1}
B) {0, 1}
C) {1, -1}
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
We have, $ f(x)=\frac{1}{1-x} $ . As at $ x=1,f(x) $ is not defined, $ x=1 $ is a point of discontinuity of f(x). If $ x\ne 1,[f(x)]=f( \frac{1}{1-x} )=\frac{1}{1-1/(1-x)}=\frac{x-1}{x} $
$ \therefore x=0,1 $ are points of discontinuity of $ f[f(x)] $ . If $ x\ne 0,x\ne 1 $
$ f[f{f(x)}]=f( \frac{x-1}{x} )=\frac{1}{1-\frac{(x-1)}{x}}=x $
BETA
