Question

find the domain: 1/√x^2-1​

Answer 1

Answer:

The domain is $(-\infty ,-1)\cup (1,\infty)$

Step-by-step explanation:

Given function is $\frac{1}{\sqrt{x^2-1}}$

For this function to be well defined, we must has $x^2-1$ positive as square root is well defined real number for non negative numbers and reciprocal of any real valued function can not be zero .

$\Rightarrow x^2-1>0\\\Rightarrow (x+1)(x-1)>0\\\Rightarrow x\in (-\infty ,-1)\cup (1,\infty)$