If {\R}= \{(x, y) ; x, y \in {\Z}, x^2+y^2 \leq 4\} is a relation in set Z, then domain of R is

Correct Answer is : {−2,−1,0,1,2}

CBSE Class 12 Math 2022 Term I Solved Paper - Question 15

Question : 15 of 50

Marks: +1, -0

{\R}= \{(x, y) ; x, y ∈ {\Z}, x^2+y^2 ≤ 4\}

is a relation in set

Z

, then domain of

R

Solution:

Explanation: Given,

R= \{(x, y): x, y ∈ Z, x^2+y^2 ≤ 4\}

\;\text " Since, "\; \;\; \begin{aligned} y\;=f(x)

y\;={√{4-x^2}} \end{aligned}

\;\text " For, "\; x=0, ± 1, ± 2, ⇒ y= ± 2, ± {√{3}}, 0

Since,
Hence, the required domain will be

0 ± 1, ± 2

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