A) {0, -1}
B) {0, 1}
C) {1, -1}
D) None of these
Correct Answer: B
Solution :
[b] 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 \[x\ne 1,[f(x)]=f\left( \frac{1}{1-x} \right)=\frac{1}{1-1/(1-x)}=\frac{x-1}{x}\] \[\therefore x=0,1\] are points of discontinuity of \[f[f(x)]\]. If \[x\ne 0,x\ne 1\] \[f[f\{f(x)\}]=f\left( \frac{x-1}{x} \right)=\frac{1}{1-\frac{(x-1)}{x}}=x\]You need to login to perform this action.
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