Question

If $f\left(x\right)=\frac{1}{x-1},$ then determine the number of points of discontinuity of $f\left[f\left\{f\left(x\right)\right\}\right].$

Answer 1

$f\left(x\right)=\frac{1}{x-1},f\left\{f\left(x\right)\right\}=\frac{x-1}{2-x}$ $f\left[f\left\{f\left(x\right)\right\}\right]=\frac{2-x}{2x-3}$
Clearly $x=1,x=2,x=3/2$ are points of discontinuity.
Ans: 3