finding inverse of function in ordered pair notation $$f: \mathbb{R} \times \mathbb{R} \mapsto \mathbb{R} \times \mathbb{R} $$
where f is defined as $$f(x,y) =(\text{somethingforx},\text{somethingfory}) $$
I dont want to post the exact question because I would like to get it on my own, but I am having trouble finding the best way to find the inverse of a function when it is given in ordered pair notation such as here. Any methods on how to proceed would be very helpful. 
Thanks 

The inverse relation of f is 
{ ( ( something for x, something for y), (x,y) ) | ((x,y) , (somethingforx, somethingfory) ) belong to f}. 
In general the inverse of R is 
{ (b,a) | (a,b) belong to R}
Here 
a = (x,y)
and
b = ( something for x, something for y)
