Finding the Inverse of a Multivariable Function

[rabbit]

Okay, so, one day in my math class I got really bored, and I wrote up this equation:
http://www.liquid-server.org/images/-pictures-63bb1c697f340f0559a1fc85e4da12da_1161299204.gif

Now, over the next few days, utilizing the awesomeness of my green pen, I calculated f(7,3,5,31) = 6.  What I wantneed now is to find the inverse of this function within its constraints, though I'm not sure how to start.  Got any ideas?

[UserLoser]

[topaz]

You hit the wrong forum

[rabbit]

.....................holy shit.  That was stupid.  Who feels like moving this?

[Rule]

Your function takes N⁴ --> R.  For a function to have an inverse, it must be a bijective mapping from its domain to its codomain.  Obviously that is not the case with your function.  Imagine how many input combinations could lead to the number "6" as output.  Now try and think of what the pre-image of "6" would look like.

[rabbit]

x, y, and z are all reduced mod N, so technically it's self limiting.  I was kind of hoping I could at least find some kind of inverse, at least from [0, n) :\