A quick Google suggests what you have.

If the code you have quoted is verbatim what you have tried, seems like you need to extract the parentheses and possibly a single or double quote, depending on the source css. The example source you have given has a single quote.

select-before(select-after(//div/@style, "backgound-image: url("), ")") 

Should be (notice the extra ' relating to url('...url'))

select-before(select-after(//div/@style, "backgound-image: url('"), "')")

But I don't think that would cause xpath to fail... It would just extract the wrong value

Edit:
Further reading suggests xpath 1.0 does have limited functionalities. But, like you, can't find anything concrete.

Asking just because I'm curious... why are you using xpath?

Also, is this for a website you control or for some else's website?

If you're rendering the page (in a browser, e2e test-runner, spider bot, etc...), have you considered running some js on the page to get the image? Something like: const imagePath = document.getElementById('exampleIdOnElement').style.backgroundImage