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Given: [tex]g(x)=\sqrt{x-4}[/tex] and [tex]h(x)=2x-8[/tex]

What is [tex]g(h(10))[/tex]?

A. [tex]2\sqrt{2}[/tex]

B. [tex]\sqrt{6}[/tex]

C. [tex]\sqrt{6}-8[/tex]

D. [tex]2\sqrt{6}-8[/tex]



Answer :

GinnyAnswer
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]

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