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Question
Find the domain of the real valued function of real variable:
(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]
Solution
(ii) Given:
(x + 1)(x -1) > 0 [ Since a2 -b2 = ( a + b)(a - b)]
x < -1 and x > 1
x ∈ (-∞ , -1) ∪ (1, ∞)
Hence, domain (f) = (- ∞ ,- 1) ∪ (1, ∞)
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