Question

Q.A relation R: Z → R defined as (x, y)£R if
$x { }^{2} + y {}^{2} = 16$
then the domain of R is?? (£=Element)​

Answer 1

Question

A relation R : Z → R defined as (x, y) ∈ R if x² + y² = 16, then the domain of R is .

Answer

↝ Domain = {0 , 4 , -4}

Solution

Now , let's see we are given with the relation that x² + y² = 16 , we have to find domain i.e all the possible inputs to satisfy the given relation with the output 16.

Possible values for x and y !!

The outcome will be 16 only with the following possibilities :-

1. x = 4 & y = 0
2. x = - 4 & y = 0
3. x = 0 & y = 4
4. x = 0 & y = -4

Thus , write them in the form of ordered pairs we have R = {(0,4) , (4,0) , (0,-4) , (-4,0)}

Now , we know that the set of first entries of the ordered pairs in R is called the domain.

∴ Domain = {0 , 4 , -4}

$\underline{\rule{200pt}{2pt}}$

Additional Information :-

$\red{ \bf \underline{Relation}}$

A set of ordered pairs obtained by the virtue of an association between two sets . Any set of ordered pairs is, therefore, a relation.

where ,

• The set of first components of ordered pairs is called the domain.
• The set of second components of ordered pairs is called the range.

$\pink{ \bf{ \underline{Function}}}$

A function is a set of ordered pairs, no two have the same first component.

✎ Note :-

By convention, the empty set is not considered a function.

Thankyou