Answer
x; no
Work Step by Step
$f(x)=\frac{1}{1-x}$
f(f(x))=$\frac{1}{1-(\frac{1}{1-x})}=\frac{x-1}{x}$,
f(f(f(x)))=$f(\frac{x-1}{x})=\frac{1}{1-(\frac{x-1}{x})}=x$,
x cannot be zero or 1 (domain calculation)
The graph is not a line as x cannot be 0 or 1.