Answer
The domain of $ f $ can be written in several ways:
$\{x|x\neq 1\},$
$\{x|x \lt 1\ or\ x \gt 1\},$
$(-\infty,1)\cup(1,\infty)$
(All real numbers except 1.)
Work Step by Step
Logarithmic functions are defined only for positive arguments.
So, the domain of f is defined with
$(x-1)^{2} \gt 0\qquad $
The square of $(x-1)$ is never negative, and it can only be zero when
$ x-1=0$
$ x=1\qquad $
$1$ is the only real number for which f is not defined
The domain of $ f $ can be written in several ways:
$\{x|x\neq 1\},$
$\{x|x \lt 1\ or\ x \gt 1\},$
$(-\infty,1)\cup(1,\infty)$
