Question

Identify the composite function and its domain

Answer 1

$f(g(x))=f(\sqrt{x-2})$
$f(g(x))=3(\sqrt{x-2})^{2}+4$
$f(g(x))=3(x-2)+4$
$f(g(x))=3x-6+4$
$f(g(x))=3x-2$

Domain:
g(x) must be greater than or equal to zero (no square roots of negative numbers) therefore x must be greater than or equal to 2.  Answer is B. 

Answer 2

The second answer is correct.
Square g(x), multiply by 3, 3x-6+4 = 3x-2.
The domain depends on the square root term which must have its argument greater or equal to zero.
Therefore x-2 >= 0, so x>=2