To give:
An example of a relation that is a function, but whose inverse is not a function.
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Answer to Problem 25E
Our required relation would be
Explanation of Solution
Given:
To form the inverse of a relation represented by a set of ordered pairs, you switch the coordinates of each ordered pair. For example, the inverse of relation
Calculation:
We know that a relationship will be also a function, when each input in the domain has exactly one specific corresponding output.
We also know that for a relation to be a function, one x- value cannot have two y -values, while two x- values can have same y- value.
To get inverse of function, the function needs to be one-to-one function. In one to one function each out-put comes from only one input that is two x- values cannot have same y- value.
The relation
The inverse of our relation would be
Therefore, our required relation would be
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