Composite functions question

State the domain of f ° g(x) and g ° f(x) if f(x) = √x and g(x) = 2x - 4

I'm just starting to work with composite functions, I have the solution to this question, but I cannot grasp how it works, can someone please give me some pointers? Here's the answer:

f ° g(x) = f(g(x))
=f(2x-4)
=√(2x-4)***
f ° g(x) is defined as long as 2x - 4 ≥ 0 ; 2x ≥4 ; x ≥ 4/2 ; x ≥ 2
∴ the domain of f ° g(x) is {x | x ≥ 2, x ∈ R}

g ° f(x) = g(f(x))
=g(√x)
=2(√x) - 4***
g ° f(x) is defined as long as x ≥ 0
∴ the domain of g° f(x) is {x | x ≥ 0, x ∈ R}

***These marked parts are where I am becoming confused, I can't figure out what is being done to 2x-4 to make √(2x-4), or what is being done to √x to make 2(√x) - 4.