Question

let R relation in N defined by R={(1+x),(1+x^2)/x<=4,x∈N} find domain of R​

Answer 1

Step-by-step explanation:

Given :-

R is a relation in N defined by R={(1+x),(1+x^2)/x<=4,x∈N}

To find :-

Find the domain of R ?

Solution :-

Given that :

R is a relation in N

R is defined as {(1+x , 1+x^2)/x≤4,x∈N}

If x≤4 then the possible values of x = 1,2,3,4

since x∈N

If x = 1 then (1+x,1+x²)

=> (1+1,1+1²)

=>(2,1+1)

=> (2,2)

If x = 2 then (1+x,1+x²)

=> (1+2,(1+2²)

=> (3,1+4)

=> (3,5)

If x = 3 then (1+x,1+x²)

=> (1+3,1+3²)

=>(4,1+9)

=> (4,10)

If x = 4 then (1+x,1+x²)

=> (1+4,1+4²)

=> (5,1+16)

=> (5,17)

Therefore, R = { (2,2),(3,5),(4,10),(5,17) }

The first coordinates in these order pairs are 2,3,4,5

Domain of R = {2,3,4,5}

The second coordinates in these order pairs are 2,5,10,17

Range of R = {2,5,10,17}

Answer:-

The domain of the relation R = { 2,3,4,5}

Used formulae:-

• The set of the first coordinates in the order pairs is called Domain.