To identify the domain it is necessary to ask "is there any value x for which the function f(x) = 9/(x-14) does not exist. The most common reason for a function to be undefined at some value x is that it results in a division by 0.
in this case when x = 14, f(14) = 9/(14-14) = 9/0 which cannot exist, so 14 is not in the domain of f(x).
domain is {x | x ∈ R; x ≠ 14}
in this case when x = 14, f(14) = 9/(14-14) = 9/0 which cannot exist, so 14 is not in the domain of f(x).
domain is {x | x ∈ R; x ≠ 14}