If R = { (x,y): x, y ∈ Z, 4 𝑥 ^2 + 9 𝑦^ 2= 36} , then (i) - Maths - Relations and Functions

Question

If R = { (x,y): x, y ∈ Z, 4 𝑥 ^2 + 9 𝑦^ 2= 36}
, then (i) Find domain of R (ii) Find range of R (iii) Represent R
by an arrow diagram (v) Write R by roster method

Rishabh Mittal · Accepted Answer

Dear Student ,

Please find below the solution to the asked query :

R= x,y : x,y∈Z , 4x2+9y2=361 4x2+9y2=369y2=36-4x2y2=36-4x29y=36-4x23For y to be defined , 36-4x2≥036≥4x29≥x2-3≤x≤3Y should be an integer 
For x=-34-32+9y2=3636+9y2=36y=0Similarly ,For x=-2 , y is not an integerFor x=-1 ,  , y is not an integerFor x=0 , y=±2For x=1 ,  y is not an integerFor x=2 , y is not an integerFor x=3 , y=0So , Domain=-3 ,0 ,32So , Range=-2, 0 , 23 Arrow diagram
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_57b2ee35b3877%20png">

4 R=-3,0 , 0,-2 , 0,2 , 3,0   ANS
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If R = { (x,y): x, y ∈ Z, 4 𝑥 ^2 + 9 𝑦^ 2= 36} , then (i) Find domain of R. (ii) Find range of R (iii) Represent R by an arrow diagram. (v) Write R by roster method.