91Ó°ÊÓ

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 $\left(1,2\right),\left(3,4\right),\left(5,6\right)\text{is}\left(2,1\right)\text{,}\left(4,3\right)\text{,}\left(6,5\right)$.

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 $\left(1,3\right),\left(7,6\right),\left(5,9\right),\left(4,3\right),\left(3,6\right)$satisfies our given conditions. Each input corresponds to exactly one out-put.

The inverse of our relation would be $\left(3,1\right),\left(6,7\right),\left(9,5\right),\left(3,4\right),\left(6,3\right)$. We can see that 3 corresponds to two values, therefore, the inverse of our relation is not a function.

The required relation would be $\left(1,3\right),\left(7,6\right),\left(5,9\right),\left(4,3\right),\left(3,6\right)$..