Question

Given, $f\left(x\right)=\frac{1}{x-1}$. Find the point(s) of discontinuity of composite function $y=f\left\{f\right(x\left)\right\}$.

Answer 1

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

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

$A+x=2$ function is not defined

So it is discontinuous at $x=2$