Question

f(x,y) = 2xy -x -y +1
Find the inverse.
The answer is: g(x) = x/(2x-1) but I can't quite figure out why. Can anyone point me in the right direction here please.

Answer 1

the inverse of a multivariable function? or is this spose to represent something in the xy plane?

Answer 2

f(x,y) = 2xy -x -y +1

with respect to x, maybe

z = 2xy -x -y +1

z = 2kx -x -k +1

z = (2k-1)x -k +1

z + k - 1= (2k-1)x

(z + k - 1)/(2k-1 )= x

(z + y - 1)/(2y-1 )= x

Answer 3

with respect to y would amount to the same results, just swapping x for y

Answer 4

http://www.wolframalpha.com/input/?i=inverse+2xy+-x+-y+%2B1+

seems to be something to it ...