f(x) = $\frac{1}{1-|x|}$
f(x) = { $\frac{1}{1-x}$ , x>=0
$\frac{1}{1+x}$ , x<0
}
$\lim_{x\rightarrow 1-}$ = +$\infty$
$\lim_{x\rightarrow 1+}$ = -$\infty$
f(1) = not defined
since LHL $\neq$ RHL $\neq$ f(1) therefore f(x) is not continous at x=1
similiarly you can check for other critical points
P.S: critical points are points where function changes its value abnormally.