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Concept

Inverse Relation

An inverse relation is a relation that interchanges the input and output values of a specific relation. In other words, it is the relation that undoes a certain relation. Consider the mapping diagram that shows a relation that takes elements from set and returns elements from set
relation and inverse relation
The relation that undoes is In this case, takes elements from set and returns elements from set Relations can also be represented by a collection of ordered pairs. Here, the inverse of a relation is obtained by interchanging the elements of the ordered pairs of the original relation.
Graphically, the inverse of a relation is a reflection across the line
inverse function
If the inverse relation of a function is also a function, then it is called an inverse function.