Contour Maps (Difficulty with an equation)

Right, I'm having difficulty with a particular contour map because I can't seem to get an answer from the multi-variable equation. I'll show you what I mean.

The contour I am trying to sketch is:

$\displaystyle g(x,y) = \frac{1}{3+x^2}$

Now I realise that, because there is no y variable in the equation, I'm looking at a contour map of verticle straight lines because I'm only going to get results for x. But when I try and find standard solutions (ie. g(x,y) = 1, 2, 3...), I always seem to run into complex results, $\displaystyle \sqrt{-a}$ where a is greater or equal to zero.

Am I using the wrong technique here (where I should really be using my understanding to justify the map) or am I making a very siiiiiiimple mistake and looking like a complete fool (which is what I think I am doing :p).