Both functions are polynomials, so they are defined everywhere.
When you compute the composite function [tex] f \circ g [/tex], you want to give the output of [tex] g [/tex] as input to [tex] f [/tex].
So, the workflow is the following:
1. Choose a number x.
2. Compute g(x). This is a new number, say z.
3. Compute f(z).
As we already stated, since f is a polynomial, it accepts every real number as input, so we must not worry about what the output of g will be. This means that the domain of the composite function is still [tex] \mathbb{R} [/tex].
As for the composite function itself, we have
[tex] (f \circ g)(x) = f(g(x)) = -2g(x) + 7 = -2(-6x+3) + 7 = 12x-6+7 = 12x+1 [/tex]
