# Find The Inverse of a Relation - Questions With Detailed Solutions

How to find the inverse of a relation given by its graph? Grade 11 examples are presented along with detailed solutions and more questions with detailed Solutions and explanations are included.

## How to find the inverse of a relation given by its graphs?

### Example 1

Sketch the graph of the inverse of the relation given by its graph below.

Solution:
Step 1: Select points on the graph of the given relation and find their coordinates: blue points shown on graph below with the following coordinates.
(8,4) , (5,2) , (4,0) , (3,-1) , (0,-2) , (-2,-4) , (-3,-5)
Step 2: Reflect the points (by switching the x and y coordinates) obtained above on the line y = x : red points.
(4,8) , (2,5) , (0,4) , (-1,3) , (-2,0) , (-4,-2) , (-5,-3)

Sketch the graph of the inverse of the given relation by connecting the inverted points as shown by the red graph below. The given graph and the inverse are reflection of each other on the line y = x.

### Example 2

Sketch the graph of the inverse of the relation given by its graph below.

Solution:
Step 1: Select and define points on the graph of the given relation by their coordinates as shown on graph below (blue points on the graph) .
(6,3) , (2,-5) , (0,-1) , (-2,-5) , (-3,-3)
Step 2: Reflect, on the line y = x, the points (by switching the x and y coordinates) obtained above as shown by the red points with coordinates.
(6,3) , (2,-5) , (0,-1) , (-2,-5) , (-3,-3)

The graph of the inverse relation is obtained by connecting the inverted points as shown below so that the given graph and the inverse are reflection of each other on the line y = x.

## More Questions: Sketch the graph of the inverse of each of the relations given by its graph below

Detailed
Solutions and explanations to these questions.
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b)

Detailed
Solutions and explanations to these questions.