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Question: Domain of the function \(\frac{1}{\sqrt{x^{2} - 1}}\) is...

Domain of the function 1x2−1\frac{1}{\sqrt{x^{2} - 1}} is

A

(−∞,−1)∪(1,∞)( - \infty, - 1) \cup (1,\infty)

B

(−∞,−1]∪(1,∞)( - \infty, - 1\rbrack \cup (1,\infty)

C

(−∞,−1)∪[1,∞)( - \infty, - 1) \cup \lbrack 1,\infty)

D

None of these

Answer

(−∞,−1)∪(1,∞)( - \infty, - 1) \cup (1,\infty)

Explanation

Solution

For domain, x2−1>0x^{2} - 1 > 0 ⇒(x−1)(x+1)>0\Rightarrow (x - 1)(x + 1) > 0

⇒x<−1orx>1\Rightarrow x < - 1\text{or}x > 1 ⇒x∈(−∞,−1)∪(1,∞)\Rightarrow x \in ( - \infty, - 1) \cup (1,\infty).