If R = {(x, y) : x, y ∈ Z, x^2 + 3y^2 ≤ 8} is a relation on the set of integers Z, then the domain R^–1 is :

Question

If $R=\{(x,y):x,y\in Z,\ x^2+3y^2\leq8\}$ is a relation on the set of integers $Z$, then the domain $R^{–1}$ is :

(1) {–1, 0, 1}

(2) {–2, –1, 1, 2}

(3) {0, 1}

(4) {–2, –1, 0, 1, 2}

Answer 1

Ans. (1) {–1, 0, 1}

Sol. ${x^2\over8}+{y^2\over8/3}\leq1$

Domain of R^–1 $\equiv$ Range of R $\equiv$ Value of y $\equiv$ {–1, 0, 1}