can anyone tell me if this is possible? please I've been breaking my head over this for 2 days. and I am actualy pretty sure its not suppose to be that hard.

F(z) = (1-e^-z)(1-e^-1) if Z<=1
F(z)=(1-e^-2(z-1))e^-1 if z>1

or
maybe it would be
F(z)=(1-e^-z)(1-e^-1)+(1-e^-2(z-1))e^-1
both of them I derive from the total probability rule but one is divided into 2 parts and on is not.
but both don't feel right and I have no idea how else to approach it.