Answer:
x ≥ 1
Step-by-step explanation:
There are no domain restrictions on a(x), so we can find the domain of the composite function by looking at that composition:
[tex](b \circ a)(x)=b(a(x)) = b(3x+1)=\sqrt{(3x+1)-4}\\\\(b \circ a)(x)=\sqrt{3x-3}=\sqrt{3(x-1)}[/tex]
The argument of the square root function must be non-negative, so we must have ...
3(x -1) ≥ 0
x -1 ≥ 0 . . . . . divide by 3
x ≥ 1 . . . . . . . add 1
The domain of b(a(x)) is x ≥ 1.
