Mathematics

Problem

Which of the following conditions must a pair of functions

f:X\to Y

and

g:Y\to X

satisfy so that each is the inverse of the other? a)

g\circ f = I_X,\; f\circ g = g

g\circ f = I_X\ \text{only}

g\circ f = I_X\text{ and }f\circ g = I_Y

g\circ f = f,\; f\circ g = g