Question

find the domain and range of the relation R : R={(x,y):x,y belong W,2x+y=8​

Answer 1

Answer:

(1,3),(2,1)

Step-by-step explanation:

The possible values of x which satisfies the given relation is the domain of the relation

The possible values of y which satisfies the given relation is the range of the relation

Given that x,y are natural numbers and the relation is x+2y=5

For x=1 , the value of y is 2

For x=3 , the value of y is 1

If x≥5, then y is negative which does not belong to naturals.

If x=2,4 then y becomes rational number which is not in naturals.

Thus, only 1 and 3 gives y as natural numbers 2 and 1.

Therefore, the domain is {1,3} and the range is {2,1}

Answer 2

$\large\underline{\sf{Solution-}}$

Given relation is

$\rm :\longmapsto\:R = \{(x,y) : 2x + y = 8 \: \forall \: x,y \: \in \: W\}$

We have given that

$\rm :\longmapsto\:2x + y = 8$

$\rm :\longmapsto\:y = 8 - 2x$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y = 8 - 2 \times 0$

$\rm :\longmapsto\:y = 8 - 0$

$\rm :\longmapsto\:y = 8$

Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:y = 8 - 2 \times 1$

$\rm :\longmapsto\:y = 8 - 2$

$\rm :\longmapsto\:y = 6$

Substituting 'x = 2' in the given equation, we get

$\rm :\longmapsto\:y = 8 - 2 \times 2$

$\rm :\longmapsto\:y = 8 - 4$

$\rm :\longmapsto\:y = 4$

Substituting 'x = 3' in the given equation, we get

$\rm :\longmapsto\:y = 8 - 2 \times 3$

$\rm :\longmapsto\:y = 8 - 6$

$\rm :\longmapsto\:y = 2$

Substituting 'x = 4' in the given equation, we get

$\rm :\longmapsto\:y = 8 - 2 \times 4$

$\rm :\longmapsto\:y = 8 - 8$

$\rm :\longmapsto\:y = 0$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 8 \\ \\ \sf 1 & \sf 6 \\ \\ \sf 2 & \sf 4\\ \\ \sf 3 & \sf 2\\ \\ \sf 4 & \sf 0 \end{array}} \\ \end{gathered}$

Hence,

$\rm :\longmapsto\:R = \{(0,8),(1,6),(2,4),(3,2),(4,0)\}$

Hence,

$\rm :\longmapsto\:Domain \: = \: \{0,1,2,3,4\}$

and

$\rm :\longmapsto\:Range \: = \: \{0,2,4,6,8\}$