Answer
The domain of the given function is $\left( -\infty ,6 \right)$.
Work Step by Step
We know that the domain is a set of values of x at which:
$f(x)=\ln (6-x)$
We know that, $(6-x)>0$
Therefore,
$-x>-6$
Or it can be written as
$x<6$
Thus, the domain of the given function is $\left( -\infty ,6 \right)$.
