1. Determine what is the rule for function [tex](f\circ g)(x).[/tex]
[tex](f\circ g)(x)=f(g(x))=f\left(\dfrac{1}{x-4}\right)=\sqrt{8\cdot \dfrac{1}{x-4}}=\sqrt{\dfrac{8}{x-4}}.[/tex]
2. The domain of the function [tex](f\circ g)(x)[/tex] - all x that sutisfy:
- [tex]x-4\neq 0;[/tex]
- [tex]\dfrac{8}{x-4}\ge 0.[/tex]
3. Solve them:
- [tex]x\neq 4;[/tex]
- [tex]x-4\ge 0\Rightarrow x\ge 4.[/tex]
Then you can state that [tex]x>4[/tex] is the domain.
Answer: x>4.
