Given `f(x)=1/(x-1)dot` Find the points of discontinuity of the composite function `f(f(x))dot`

Answer

Points of discontinuity of `y=f(f(x))` is when `x=2`.

Explanation

$$ \begin{aligned} &f(x)=\frac{1}{x-1} \\ \\ &f(f(x))=\frac{1}{\frac{1}{x-1}-1}=\frac{x-1}{1-x+1}=\frac{x-1}{2-x} \end{aligned} $$
Points of discontinuity of `y=f(f(x))` is when `x=2`.