The domain of a composite function
<span>
</span><span>is, technically speaking, the set of those inputs </span>
<span> in the domain of </span>
<span> for which </span>
<span> is in the domain of </span>
. What this is really saying, though, is that the domain is for those
that overlap in both functions, or that are defined for both
and
. You can write {
∩<span> </span>
}.
For this specific example, the domain of
is {all real numbers
}. The domain of
is {
}. These overlap for all
such that
, so the domain of
is {
}.