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.

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Please find below the solution to the asked query :

R= x,y : x,yZ , 4x2+9y2=361 4x2+9y2=369y2=36-4x2y2=36-4x29y=36-4x23For y to be defined , 36-4x20364x29x2-3x3Y 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


4 R=-3,0 , 0,-2 , 0,2 , 3,0   ANS...
 
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