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If f(x)=(1)/(1-x), then the points of d...

If `f(x)=(1)/(1-x)`, then the points of discontinuity of the function `f[f{f(x)}]` are

A

{0}

B

{0, 1}

C

{1, -1}

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `f(x)=(1)/(1-x)`
As at x = 1, f(x) is not defined. So, x = 1 is a point of discontinuity of f(x).
If ` x ne 1, f[f(x)] =f((1)/(1-x)) =(1)/(1-1//(1-x))=(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((x-1)/(x))=(1)/(1-((x-1))/(x))=x`
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