You must do in this case is composition of both functions:
a (x) = 3x + 1
b (x) = root (x-4)
Making the composition
b (a (x)) = root ((3x + 1) -4)
Rewriting:
b (a (x)) = root (3x-3)
b (a (x)) = root (3 (x-1))
Answer:
The domain of the function is:
x> = 1
Equivalently:
[1, inf)