Concepts of Square root
f(x)= \[\sqrt{^{x^{2}-1}} \]
Here doamin is set of values of x for which f(x) gives valid output.
For any square root function to be defined , quantities within the square root must be non negative.
So \[x^{2} -1 \] \[\geq \] 0 .
hence (x-1) (x+1) \[\geq \] 0
which is true only if x belongs to (-∞ , -1] U [1,∞).
Similarly for \[\frac{1}{\sqrt{^{x^{2}-1}} } \]
it holds good for (-∞ , -1) U (1,∞).
In this case -1 and 1 are not included as the function becomes zero at these points.
