Final answer:
The restrictions on the domain of the composite function g∘h, where g(x) = √(x-4) and h(x) = 2x - 8, require that x must be greater than or equal to 4.
Step-by-step explanation:
The question is about finding the restrictions on the domain of the composite function g∘h. In this case, g(x) is the square root function, which requires its argument to be non-negative because square roots of negative numbers are not real numbers. However, since we are dealing with the composition of two functions, the output of h(x), which is given by 2x - 8, must be non-negative because it becomes the input for g(x) when creating the composite function g∘h.
To determine the domain restrictions for g∘h, we set the inside of the square root to be greater than or equal to zero, which means 2x - 8 must be ≥ 0. Solving this inequality for x gives us x ≥ 4. Hence, the restriction on the domain of g∘h is that x must be greater than or equal to 4.