I know it's a dumb question, but could you please show me the right logic behind those calculations in order to find the domains of the following composite questions - I found the answers, but eventually making a lot of mistakes, so I am not sure in how I solved them; I just want to make clear once and forever on those points. Thanks

f(x) = sqrt(3x-8)

D = [8/3, INF)

and

g(x) = 5x^2 -1

D= R

1. (f o g)(x) = f(g(x)) =f(5x^2 - 1) = sqrt(3(5x^2 - 1) - 8) = 15x^2 – 3 – 8 = sqrt(15x^2 -11)

D= (-INF, -sqrt(11/15)]U[sqrt(11/15), INF)

2. (g o f)(x) = g(f(x)) = 5(sqrt(3x - 8))^2 -1 = 15x -40 – 1 = 15x-41;

D=[8/3, inf)

3. (f o f)(x) = sqrt(3(sqrt(3x - 8)) - 8)

D=[136/27, INF)