You can put this solution on YOUR website!
The domain of the function is the set of allowable values for x. There are several reasons for disallowing values for x:
Denominators must not be zero!!
Radicands (the expression in an radical) of even-numbered roots must never be negative (for Real-valued functions).
Arguments to logarithms must never be zero or negative. (IOW, they must be positive.)
Other undefined expressions like
The only one of these your function has is an even-numbered root. (Square roots are 2nd roots.) So the only thing we have to avoid is a negative value for the radicand. Put another way, our domain must ensure that the radicand, x+2, is equal to zero or positive. In Math terms, the domain is the solution to:
Solve this and you have your domain.
(