ANSWER
The correct answer is C
EXPLANATION
This is the composition the two functions
We have
[tex]a(x) = 3x + 1[/tex]
and
[tex]b(x) = \sqrt{x - 4} [/tex]
[tex](b \circ \: a)(x) = b(a(x)) [/tex]
[tex](b \circ \: a)(x) = b(3x + 1) [/tex]
We substitute to obtain,
[tex](b \circ \: a)(x) = \sqrt{(3x + 1) - 4} [/tex]
[tex](b \circ \: a)(x) = \sqrt{3x - 3} [/tex]
The domain of this function can be found by solving,
[tex] 3x - 3 \geqslant 0[/tex]
This implies that
[tex]3x \geqslant 3[/tex]
Or
[tex]x \geqslant 1[/tex]
In interval notation, we have,
[tex][1, \infty )[/tex]
The correct answer is option C
