find the domain of f(x)=((2x+7)/([2−x^2 ]))


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Question Number 31811 by NECx last updated on 15/Mar/18

$f i n d t h e d o m a i n o f$ $f (x) = \frac{2 x + 7}{[2 - x^{2}]}$
Commented by Tinkutara last updated on 15/Mar/18

$D o m a i n = R - {[- \sqrt{2}, - 1) \cup (1, \sqrt{2}]}$
Commented by NECx last updated on 15/Mar/18

$p l e a s e s h o w w o r k i n g s$
	Answered by Tinkutara last updated on 16/Mar/18
	$First consider [2−x^2 ]=0 0≤2−x^2 <1 1<x^2 ≤2 x∈[−(√2),−1)∪(1,(√2)] ∴ Domain=R−{[−(√2),−1)∪(1,(√2)]}$
	$F i r s t c o n s i d e r [2 - x^{2}] = 0$ $0 ⩽ 2 - x^{2} < 1$ $1 < x^{2} ⩽ 2$ $x \in [- \sqrt{2}, - 1) \cup (1, \sqrt{2}]$ $∴ D o m a i n = R - {[- \sqrt{2}, - 1) \cup (1, \sqrt{2}]}$
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