Given the relation #(2,3)#, #(3,4)# what is the inverse of this relation?

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Answer 1 · 2017-12-06T15:41:15

#color(blue)({(3, 2), (4,3)})#

You can also observe the behavior of the relation and it's inverse in the graph.

A Relation is a set of ordered pairs.

We have the following relation as a set of ordered pairs:

#color(blue)({(2, 3), (3,4)}#

How do we define the Inverse of a Relation?

The Inverse of a Relation is a set of ordered pairs that is the exact inverse of the set of ordered pairs of the original relation.

So, to find the inverse of a relation we must flip over each one of our ordered pair. That is switch #x# and the corresponding #y# values.

When we draw the graph of the relation and it's inverse , we can observe that the values are reflected over the line #color(green)(y = x)#

enter image source here

I hope this helps.