First, I'll say that english isn't my first language and that I'm not studying math in english, so I'll probably say some stuff wrong.
Anyway, what I was wondering is how to find the inverse function of a function that has multiple variables? Because in $\mathbb{R}^{2}$ (in two dimensions), it's pretty simple, you can just exchange x and y and then isolate y. But is it possible in $\mathbb{R}^{3}$, in $\mathbb{R}^{4}$ or even in $\mathbb{R}^{n}$ ?
To make it clearer, take the simplest function possible, like: $z=x+y$ (another one could do the job too, I just didn't have a particular function in mind) What will be the inverse function? In my head the whole concept of inverse function in $\mathbb{R}^{n}$, when $n\gt2$, isn't clear..
If you can help me or if I'm not clear enough, let me know! Thanks!