I'm designing a t-shirt, and I'm trying to get an effect where an object's color is the negative of whatever color is behind it.

So in this case, I'm trying to get the word "focus" to be white where the spiral is black, and black where the spiral is white. I've tried some stuff with transparency but it's not working out.

Hi chillychili,

Welcome to the forum!

There may be other ways to do what you want, but this is what I came up with.
The spiral -- first do Object to Path, then Stroke to Path
The text -- Object to path
Next select everything and do Path menu > Combine. If you don't automatically see what you want after this last step, then open the Fill and Stroke dialog. On the fill tab, there are 2 roughly heart-shaped icon/buttons. Click the one with a hole in it, then you should see negative effect.

It worked. Thanks!