[tex]g(x) = \sqrt{x-4}[/tex] and h(x)= 2x-8
g o h is a composition function
First we find g o h
g o h is g(h(x))
We plug in h(x) in g(x)
We replace x with 2x-8 in g(x)
[tex]g(h(x)) = g (2x-8) = \sqrt{2x-8-4} = \sqrt{2x-12}[/tex]
[tex]g(h(x)) = \sqrt{2x-12}[/tex]
To find domain we look at the domain of h(x) first
Domain of h(x) is set of all real numbers
now we look at the domain of g(h(x))
Negative number inside the square root is imaginary. so we ignore negative number inside the square root
So to find domain we set 2x - 12 >=0 and solve for x
2x - 12 >=0
add both sides by 12
2x >= 12
divide both sides by 2
x > = 6
