Question

Find the domain of the real valued function of real variable:

(ii) \[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]

 

Answer 1

(ii) Given: 

\[f\left( x \right) = \frac{1}{\sqrt{x^2 - 1}}\]

Clearly, f (x) is defined for x²  -1 > 0 .
(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, ∞)