How do you find the domain and range of #sqrt(x^2- 4)#?
The best and fastest way is to learn how do parental functions look like and how does the formula look like and then use it.
The domain: square root must be greater or equal to 0:
That happens only when f(x)>0......everything that is above x axis, like this:(i usually draw a simple picture of quadratic function)
There are many ways to find the range. I do it like this: parental square root starts in
As you can see. It is always positive. so the range is: