ANSWER
[tex][1, \infty ][/tex]
EXPLANATION
The given functions are:
[tex]a(x) = 3x + 1[/tex]
[tex]b(x) = \sqrt{x - 4} [/tex]
We want to find the domain of the composite function;
[tex](b \circ \: a)(x) = b(a(x))[/tex]
[tex](b \circ \: a)(x) = b(3x + 1)[/tex]
[tex](b \circ \: a)(x) = \sqrt{3x + 1 - 4} [/tex]
This simplifies to,
[tex](b \circ \: a)(x) = \sqrt{3x - 3} [/tex]
This function is defined for
[tex]3x - 3 \geqslant 0[/tex]
[tex]3x \geqslant 3[/tex]
[tex]x \geqslant 1[/tex]
This can be rewritten as,
[tex][1, \infty ][/tex]
