Question

Match the sets of points representing one-to-one functions with the sets of points representing their inverse functions.

Tiles
h = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

g = {(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)}

f = {(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)}

i = {(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)}


Pairs
h-1 = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}

i -1 = {(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)}

g-1 = {(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)}

f -1 = {(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)}

Answer 1

Given a set of points representing a function, the inverse is the interchange of the set of points. i.e. given point (a, b), the inverse is point (b, a).

Thus, given

`h = \{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)\}`,
the inverse is

`h^(-1) = \{(1,\1), (2,\2), (3,\3), (4,\4), (5,\5), (6,\6)\}`

Given

`g = \{(1,3), (2,6), (3,9), (4,12), (5,15), (6,18)\}`
the inverse is

`g^(-1) = \{(3,1), (6,2), (9,3), (12,4), (15,5), (18,6)\}`

Given

`f = \{(1,2), (2,3), (3,4), (4,5), (5,6), (6,7)\}`
the inverse is

`f^(-1) = \{(2,1), (3,2), (4,3), (5,4), (6,5), (7,6)\}`

Given

`i = \{(1,1), (2,3), (3,5), (4,7), (5,9), (6,11)\}`
the inverse is

`i^(-1) = \{(1,1), (3,2), (5,3), (7,4), (9,5), (11,6)\}`