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Solutions to Inverse of Relations

Detailed solutions to questions on how to find the inverse of relations are presented.

Sketch the graph of the inverse of each of the relations given by its graph below.

a)

inverse of relation for question 1



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.

(4,2) , (2,2) , (1,-1) , (0,-2) , (-1,-1) , (-2,-4)

Step 2: Reflect, on the line y = x, by switching the x and y coordinates of the points obtained above to obtain the red points.

(2,4) , (2,2) , (-1,1) , (-2,0) , (-1,-1) , (-4,-2)

points on graph of relation for question 1



The inverse of the given relation is obtained 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.

inverse of relation for question 1





b)

inverse of relation for question 2



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.

(5,6) , (4,1) , (2,-1) , (0,-3) , (-1,-8)

Step 2: Reflect the points (by switching the x and y coordinates) obtained above on the line y = x : red points.

(6,5) , (1,4) , (-1,2) , (-3,0) , (-8,-1)

points on graph of relation for question 2



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

inverse of relation for question 2



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Updated: 20 January 2017 (A Dendane)

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