Question

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Answer 1

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)

Answer 2

The domain of a(x) here is all real numbers x, or (–∞, ∞). 

The domain of b(x) is [4, ∞).

The square-root function is defined when the radicand is greater than OR equal to zero, so we write $x-4 \geq 0$, being careful to include zero. $x \geq 4$. 

These two domains overlap for [4, ∞).

The domain is [4, ∞)