Question
Which description best explains the domain of
?
the elements in the domain of
for which
is defined
the elements in the domain of
for which
is not zero
the elements in the domain of
for which
is defined
the elements in the domain of
for which
is not zero
the elements in the domain of
the elements in the domain of
the elements in the domain of
the elements in the domain of
Ask by Lee Nunez. in the United States
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The domain of
includes all
in the domain of
where
is defined.
Solution
-
The domain of the composite function
consists of all values such that: -
is in the domain of , and -
is in the domain of .
-
-
This means that for every
we choose, must be defined. -
Therefore, the best description is:
- The elements in the domain of
for which is defined.
- The elements in the domain of
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The Deep Dive
The domain of
consists of the elements in the domain of
for which
is defined. This means any input
you choose must first be valid for
, and the output
must also fall within the domain of
to ensure
can be computed.
To put it simply, when chaining two functions, it’s crucial that the output of the first function (in this case,
) must be a valid input for the second function (i.e.,
). So think of it as a relay race—each runner (function) must stay in their lane and pass the baton (output) smoothly!