Question

Given functions g(x)=x+14​ and f(x)=x−7, state the domains of the following functions using interval notation. Domain of f(x)g(x)​ : Domain of g(f(x)) : Domain of f(g(x)) :

Answer 1

The domains of f(x)g(x), g(f(x)), and f(g(x)) are all real numbers.

Step-by-step explanation:

Domain of f(x)g(x):

To find the domain of f(x)g(x), we need to consider the restrictions on both f(x) and g(x). The domain of f(x) is all real numbers, as there are no restrictions. The domain of g(x) is also all real numbers. Therefore, the domain of f(x)g(x) is all real numbers.

Domain of g(f(x)):

To find the domain of g(f(x)), we need to consider the restrictions on f(x). The domain of f(x) is all real numbers. Since g(x) contains no restrictions, the domain of g(f(x)) is also all real numbers.

Domain of f(g(x)):

To find the domain of f(g(x)), we need to consider the restrictions on g(x). The domain of g(x) is all real numbers. Since f(x) contains no restrictions, the domain of f(g(x)) is also all real numbers.

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