SOLUTION: Question is: Give the domain of square root of x + 1 over x in interval notation. My first answer was (-infinity, 0) U (0, infinity). I got the second part right but I did not ge

Question is: Give the domain of square root of x + 1 over x in interval
notation. My first answer was (-infinity, 0) U (0, infinity). 
I got the second part right but I did not get the first part 
of the answer right. I know that the reciprocal function 
f(x) = 1/x contains the domains of (-infinity, 0) U (0,infinity)
but apparently this does not help me. Can anyone help?  
        _____
       Öx + 1   
f(x) = -------
          x 

Start out by drawing a numberline

------------------------------------------
-4   -3   -2   -1    0    1    2    3    4

Two things affect the domain:

1. The denominator must not be 0.
2. Even root radicands (expressions under even-root radicals)
   must not be negative.

We must rule out denominator = x = 0, so we put )( on the number line at 0:

---------------------)(--------------------
-4   -3   -2   -1    0    1    2    3    4

Since square root is an even root we must require that the 
radicand, x + 1 not be negative, which means that it is either
0 or greater than 0, so we have this inequality:

         x + 1 > 0
             x > -1

The domain will include the part of the number line at or to 
the right of -1, except of course for 0.  We put [ at -1 and 
shade up to 0, skip over 0 and shade the part to the right of 0:


----------------[====)(===================>
-4   -3   -2   -1    0    1    2    3    4

This translates to interval notation as

                [-1, 0) U (0, oo)


Edwin