Is the function f Z2 rigth arrow Z2 defined by fx y x y x

Is the function f: Z^2 rigth arrow Z^2 defined by f(x, y) = (x - y, -x) invertible? Fully justify your answer. If the function is invertible. determine its inverse.

Solution

for this we have to solve :

u-v =x

and u= -x

On Solving, we get

u =-x and v =-2x

Since it is solvable hence inverse exits

The inverse hence is

f(x,y) = (-x,-2x)