Answer:
[tex]g(h(10)) = 2\sqrt 2[/tex]
Step-by-step explanation:
Given
[tex]g(x) = \sqrt {x - 4[/tex]
[tex]h(x) = 2x - 8[/tex]
Required
[tex]g(h(10))[/tex]
First, calculate [tex]g(h(x))[/tex]
We have:
[tex]g(x) = \sqrt {x - 4[/tex]
This gives:
[tex]g(h(x)) = \sqrt {h(x) - 4[/tex]
Substitute [tex]h(x) = 2x - 8[/tex]
[tex]g(h(x)) = \sqrt {2x - 8 - 4[/tex]
[tex]g(h(x)) = \sqrt {2x - 12[/tex]
Substitute [tex]x = 10[/tex]
[tex]g(h(10)) = \sqrt {2*10 - 12[/tex]
[tex]g(h(10)) = \sqrt {20 - 12[/tex]
[tex]g(h(10)) = \sqrt {8\\[/tex]
Split
[tex]g(h(10)) = \sqrt {4} * \sqrt 2[/tex]
This gives
[tex]g(h(10)) = 2\sqrt 2[/tex]
