Question

Given g(x)=Squareroot x-4 and h(x)=2x-8, what are the restriction on the domain of gofh?

Answer 1

The square root has to be >= to zero, so g(h(x)) = SQRT((2x-8)-4)
where 2x-12>=0 or x>=6

Answer 2

$g(f(x)) = \sqrt{(2x - 8) - 4}$
$= \sqrt{2x - 12}$

Now, there's a restriction inside the square root
Thus, 2x - 12 ≥ 0
2x ≥ 12
x ≥ 6