## About "How to find the domain and range from a relation"

How to find the domain and range from a relation :

Let A and B be any two non empty sets. A function f from A to B is a rule of correspondence that assigns each element x  A to a unique element y  B. We denote y = f (x) to mean y is a function of x.

The set A is called the domain of the function and set B is called the co-domain of the function. Also, y is called the image of x under f and x is called a pre image of y.

The set of all images of elements of A under f is called the range of f .

Note that the range of a function is a subset of its co-domain.

Let us look into some example problems to understand the above concept.

Example 1 :

Which of the following relations are functions from

A = { 1, 4, 9, 16 } to B = { –1, 2, –3, –4, 5, 6 }

In case of a function, write down its domain and range.

(i) f1 = { (1, –1), (4, 2), (9, –3), (16, –4) }

Solution :

To check whether it forms a function or not, let us draw a arrow diagram. From the above arrow diagram, we come to know that every element in A has images in set B.So the above relation forms a function.

Domain is the set of elements of set A

Domain  =  {1, 4, 9, 16}

Range is the set of elements of set B which has preimage with set A.

Range  =  {-1, 2, -3, -4}

Co domain  =  { –1, 2, –3, –4, 5, 6 }

(ii)  f2 = { (1, –4), (1, –1), (9, –3), (16, 2) }

Solution :

To check whether it forms a function or not, let us draw a arrow diagram. Since 1 is having more than one image, it is not a function.

(iii)  f3 = { (4, 2), (1, 2), (9, 2), (16, 2) }

Solution :

To check whether it forms a function or not, let us draw a arrow diagram. Every element in set A has images in set B. Hence it is a function.

Domain  =  {1, 4, 9, 16}

Range  =  { 2 }

(iv)  f4 = { (1, 2), (4, 5), (9, –4), (16, 5) }

Solution :

To check whether it forms a function or not, let us draw a arrow diagram. Every element in set A has images in set B. Hence it is a function.

Domain  =  {1, 4, 9, 16}

Range  =  { 2, -4, 5 } After having gone through the stuff given above, we hope that the students would have understood "How to find the domain and range from a relation".

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