# How do you find the domain of #h(x)=sqrt(4-x)+sqrt(x^2-1)#?

##### 1 Answer

Jan 6, 2016

Domain of

#### Explanation:

Domain is all possible allowable

There are generally 2 cases that are not allowed in real functions :

- Even square roots of negative numbers. (Not defined in
#RR# ). - Division by zero. (Not defined at all).

In this case there are no divisions (denominators) in

Doing so, it becomes clear that the first term is only negative if

So #

Hence the domain is

The graph makes it clear :

graph{sqrt(4-x)+sqrt(x^2-1) [-7.28, 10.5, -1.93, 6.95]}