Final answer:
The domain of (f + g)(x) is x ≥ -6, and the domain of f(g(x)) is also x ≥ -6. Therefore, the domain of f(g(x)) is the same as the domain of f(x), which is x ≥ -6.
Step-by-step explanation:
To find the domain of the functions (f + g)(x) and f(g(x)), we need to consider the restrictions on the input values for each function.
(i) (f + g)(x) = f(x) + g(x)
The function f(x) = √(x + 6) is defined for x + 6 ≥ 0, which means x ≥ -6. The function g(x) = 1/2 is defined for all real numbers. Therefore, the domain of (f + g)(x) is x ≥ -6.
(ii) f(g(x)) = √(g(x) + 6)
The function g(x) = 1/2 is a constant value and does not introduce any restrictions on the input values. Therefore, the domain of f(g(x)) is the same as the domain of f(x), which is x ≥ -6.
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