Question

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Answer 1

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, ∞)

Answer 2

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)