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Answer: [tex]x\geq 6[/tex]
Step-by-step explanation:
Given
[tex]g(x)=\sqrt{x-4}\\h(x)=2x-8[/tex]
Now, g of h i.e. [tex]g(h(x))[/tex]
Put h(x) in place of x in g(x)
[tex]\Rightarrow g(h(x))=\sqrt{(2x-8)-4}\\\\\Rightarrow g(h(x))=\sqrt{2x-12}[/tex]
Now, the value inside square root must be greater than zero
[tex]\Rightarrow 2x-12\geq 0\\\\\Rightarrow 2x\geq 12\\\\\Rightarrow x\geq 6[/tex]