Answer
Domain = $\mathbb{R}\backslash\{6\}$ or $\{x\in \mathbb{R}\ |\ x\neq 6\}$
Work Step by Step
The domain of a real function ( a function defined on real numbers)
is the set of numbers for which f(x) is defined.
$f(x)=\displaystyle \frac{7}{6-x}$ can be calculated for any real number,
except for those yielding a zero in the denominator.
$x=6$ must be excluded from the domain.
Domain = $\mathbb{R}\backslash\{6\}$ or $\{x\in \mathbb{R}\ |\ x\neq 6\}$