Nice job on figuring it out!
I think it is still worthwhile to include an explanation in this thread so that other students who may have the same question can also gain insight into natural domain.
Essentially, when a function
)
is defined and the domain is not stated explicitly, the domain is assumed to be the largest set of real
values for which the formula gives real
values. In other words, the natural domain comprises the
values for which the function is defined, i.e. defined by the function rather than by a question.
For example, the natural domain of
)
is
.
On the other hand, a domain (which may also be called a restricted domain) is imposed by a question or by part of a question.
For example, the natural domain of the function
is all real
. However, a question could specify or restrict the domain to
for instance.
