The value of g(h(10)) is [tex]2 \sqrt{2}[/tex]
Step-by-step explanation:
Given that,
[tex]g(x)=\sqrt{(x-4)}[/tex] and h(x) = 2x-8
To find g(h(10)) first find h(10) that implies
h(x) = 2x-8
[tex]h(10)=(2 \times 10)-8[/tex]
h(10) = 20 - 8
h(10) = 12
Now, g(h(10)) = g(12)
[tex]g(x)=\sqrt{(x-4)}[/tex]
[tex]g(12)=\sqrt{(12-4)}[/tex]
[tex]g(12)=\sqrt{8}[/tex]
[tex]\sqrt{8}[/tex] Can be written as [tex]=\sqrt{2 \times 2^{2}}[/tex]
[tex]g(12)=\sqrt{2} \times \sqrt{2^{2}}[/tex]
[tex]g(12)=2 \sqrt{2}[/tex]
[tex]\therefore[/tex][tex]g(h(10))=2 \sqrt{2}[/tex]
Therefore [tex]g(h(10))=2 \sqrt{2}[/tex] for the Given g(x) = root x-4 and h(x) = 2x-8.
