Find the inverse of a function like $f(t,x,y)=(\frac{x}{t+1},\frac{y}{t+1})$

Question

How would I find the inverse of a function like $f(t,x,y)=(\frac{x}{t+1},\frac{y}{t+1})$? The usual trick with replacing x and y and than solving for y doesn't really work here does it?

$(t,x,y)\in \Bbb H^2$

I'd prefer a hint over a full answer, so I can try to find the final solution myself.

Answer 1

This function is not invertible because it is not injective; for example:

$$f(0,1,1)=f(1,2,2)=... =(1,1,1)$$