Find-the-domain-and-range-of-relation-a-R-x-y-y-x-2-6-b-R-x-y-x-2-y-2-1-

Question Number 75456 by peter frank last updated on 11/Dec/19

F i n d t h e d o m a i n a n d

r a n g e o f r e l a t i o n

(a) R = {(x, y) : y = \sqrt{x^{2} - 6}}

(b) R = {(x, y) : x^{2} - y^{2} = 1}

Answered by Kunal12588 last updated on 11/Dec/19

(a) x \in (- \infty, - \sqrt{6}] \cup [\sqrt{6}, \infty)

y \in [0, \infty) o r R_{+}

(b) x \in (- \infty, - 1] \cup [1, \infty)

y \in (- \infty, \infty) o r R

Answered by vishalbhardwaj last updated on 11/Dec/19

(a) y^{2} = x^{2} - 6

\Rightarrow x = \pm \sqrt{y^{2} + 6}

\Rightarrow x ⩾ \sqrt{6}, \forall y \in R

\Rightarrow x \in [\sqrt{6,} \infty)

and y \in [0, \infty)