Question

Is (2,3),(-4,5),(2,7),(7,-2) a function?

Answer 1

A relation between two sets is said to be a function iff each element of the first set has only one image ( the element of the other set)

To be more specific, Any element in the domain should correspond to only one element in the range.

Given, Relation R = { (2,3),(-4,5),(2,7),(7,-2)}

2 is related to 3

-4 is related to 5

2 is again related to 7

7 is related to - 2

Since, The element 2 from the domain ( X - coordinate, Abscissa) in linked to two elements 3, 7 ( Y - Coordinate, Ordinate)

This is not a function!

___________________________________________

But, Remarkably, The inverse of this relation comes out to be a function.

Inverse relation R' = { (3, 2), (5,-4), (7,2),(-2, 7)}

Now,

3 has one image " 2"

5 has one image " - 4"

7 has one image " 2".

-2 has one image " 7"

Elements from the domain are connected to single element in the range, Hence R' is a function