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Q)

If $f(x)=\large\frac{1}{1-x}$,find the points of discontinuity of the composite function $y=f(f(f(x)))$

$(a)\;0,0\qquad(b)\;0,1\qquad(c)\;1,1\qquad(d)\;None\;of\;these$

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A)
$f(x)$ is discontinuous at $x=1$
Now $f(f(x))=\large\frac{1}{1-\Large\frac{1}{1-x}}$
$\Rightarrow \large\frac{x-1}{x}$ which is discontinuous at $x=0$
But $f(f(f(x)))=\large\frac{1}{1-\Large\frac{x-1}{x}}$$=x$
Which has no point of discontinuity.
Hence $x=0,1$ are the only points of discontinuity.
Hence (b) is the correct answer.
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