Question

Given $f\left(x\right)=\frac{1}{x-1}$ . Find the points of discontinuity of the composite function $y=\left[f\left\{f\left(x\right)\right\}\right]$

Answer 1

$f\left(x\right)=\frac{1}{x-1}$

$f\left(f\right(x\left)\right)=\frac{1}{\frac{1}{x-1}-1}=\frac{x-1}{1-x+1}=\frac{x-1}{2-x}$

Points of discontinuity of $y=f\left(f\right(x\left)\right)$ is when $x=2$.