I need to find the composition of a function and its inverse so I have the identity function in return. My problem is that I don't seem to undestand how to proceed algebraically.
I have a function with couples, let's say: $f(x,y)=(x+y,\;2x-2y)$
The inverse would be: $f^{-1}(x,y)=(2x-2y,\;x+y)$
Now, to prove that $f^{-1}$ $\circ$ $f$ = identify function is where I'm getting confused.
I've been trying to solve this way: $f^{-1}(f(x,y)) = 2(x+y)-2y,x+(2x-2y)$ because I thought it was the way to proceed but it gives me an incorrect result.
Anyone could point me in the right direction? Thanks!