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Given: g(x) = Nx-4 and h(x) = 2x-8.
What are the restrictions on the domain of g ∘ h?

User Paddyd
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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.

User Tim Groeneveld
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