In Problems 35-44, verify that the functions and are inverses of each other by showing that and . Give any values of that need to be excluded from the domain of and the domain of .
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To find: Verify that the functions and are inverses of each other by showing that and . Give any values of that need to be excluded from the domain of and the domain of .
Answer to Problem 42AYU
Solution:
The given functions and are verified.
The values of to be excluded from the domain of and the domain of are .
Explanation of Solution
Given:
By domain of a Composite Function,
The domain of a composite function is the set of those inputs in the domain of for which is in the domain of .
Calculation:
The domain of is .
The domain of is .
From those inputs, , in the domain of for which is in the domain of . That is, exclude those inputs, , from the domain of for which is not in the domain of . The resulting set is the domain of . i.e., .
We know the composition of and is defined as.
Also
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