Answer:
[tex]x \ge 2[/tex] and [tex]x \ne 4[/tex].
Step-by-step explanation:
In the given function [tex]f(x) = (\sqrt{x - 2}) / (x - 4)[/tex], there are two constraints:
For a value of [tex]x[/tex] to be in the domain of this function, both requirements must be satisfied. Simplify both inequalities to obtain their intersection:
[tex]x \ge 2[/tex] and [tex]x \ne 4[/tex].