Final answer:
The domain of the composition of the functions g(x) = Nx - 4 and h(x) = 2x - 8, noted as g ∘ h, is all real numbers, assuming that N is a real number and does not cause the function to be undefined.
Step-by-step explanation:
The composition of two functions, g ∘ h, means to apply the function h first and then apply the function g to the result. For g(x) = Nx - 4 and h(x) = 2x - 8, the composition g ∘ h would be g(h(x)).
This means we substitute h(x) into g(x), resulting in g(2x - 8), which simplifies to N(2x - 8) - 4.
The domain restrictions for g ∘ h would be the same as those for h, because h is applied first.
Since there are no restrictions given for h(x), we do not have any initial restrictions for g ∘ h.
However, if we consider any potential restrictions on N that would affect the domain, we must note that as long as N is a real number, it would not impose any further restrictions on the domain.
Therefore, the domain of g ∘ h is all real numbers, assuming N is a real number and does not cause the function to be undefined.