To solve the problem, we need to find \( g(h(10)) \) given the functions \( g(x) = \sqrt{x-4} \) and \( h(x) = 2x - 8 \).
First, we need to compute \( h(10) \):
[tex]\[h(x) = 2x - 8\][/tex]
[tex]\[h(10) = 2(10) - 8\][/tex]
[tex]\[h(10) = 20 - 8\][/tex]
[tex]\[h(10) = 12\][/tex]
Next, we need to find \( g(h(10)) \):
[tex]\[h(10) = 12\][/tex]
[tex]\[g(x) = \sqrt{x - 4}\][/tex]
[tex]\[g(12) = \sqrt{12 - 4}\][/tex]
[tex]\[g(12) = \sqrt{8}\][/tex]
[tex]\[g(12) = 2\sqrt{2}\][/tex]
Therefore, \( g(h(10)) = 2\sqrt{2} \).
The correct answer is:
[tex]\[ \boxed{2 \sqrt{2}} \][/tex]
