Final answer:
To determine the domain for the function ((f)/(g))(x) where f(x)=x+5 and g(x)=x³/², we need to consider the domains of both f(x) and g(x). Since g(x) cannot take negative values due to the square root, the domain of ((f)/(g))(x) is all non-negative real numbers, x ≥ 0.
Step-by-step explanation:
To find the domain for the combined function ((f)/(g))(x), where f(x)=x+5 and g(x)=x³/², we first need to consider the individual domains of f(x) and g(x). Since f(x) is a linear function, its domain is all real numbers. However, for g(x), which involves a square root (x³/² = √x), the domain must exclude negative numbers to remain real.
Therefore, the domain of g(x) is x ≥ 0. The domain of the combined function ((f)/(g))(x) is then the intersection of the individual domains, which is also x ≥ 0 since there is no restriction from f(x) beyond what is already restricted by g(x).