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Example Question #51 : Properties Of Functions And Graphs
Define the functions and
on the set of real numbers as follows:
Give the natural domain of the composite function .
Possible Answers:
Correct answer:
Explanation:
The natural domain of the composite function is defined to be the intersection of the two sets.
One set is the natural domain of . Since
is defined to be the square root of an expression, the radicand must be nonnegative. Therefore,
This set is .
The other set is the set of numbers that the function pairs with a number within the domain of
. Since the radicand of the square root in
must be nonnegative,
For to fall within this set:
This set is .
, which is the natural domain.
Sumit
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