To understand the domain of the composite function \( g(f(x)) \), we need to consider the definitions of \( f(x) \) and \( g(x) \).
The domain of \( g(f(x)) \) will be influenced by the following:
- The domain of \( f(x) \): \( f(x) \) must be defined for all \( x \) in its domain.
- The output of \( f(x) \) must fall within the domain of \( g(x) \): For \( g(f(x)) \) to be defined, the value \( f(x) \) must be an element of the domain of \( g(x) \).
Given these considerations, the best description that fits is:
the elements in the domain of \( f(x) \) for which \( g(f(x)) \) is defined.
This is because \( g(f(x)) \) is defined only for those \( x \) such that \( f(x) \) is within the domain of \( g \).