In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f ( g ( x ) ) = x and g ( f ( x ) ) = x . Give any values of x that need to be excluded from the domain of f and the domain of g . f ( x ) = x ; g ( x ) = x
In Problems 35-44, verify that the functions f and g are inverses of each other by showing that f ( g ( x ) ) = x and g ( f ( x ) ) = x . Give any values of x that need to be excluded from the domain of f and the domain of g . f ( x ) = x ; g ( x ) = x
Solution Summary: The author explains that the functions f and g are inverses of each other.
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
.
;
Expert Solution & Answer
To determine
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 40AYU
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., .
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