I did the same thing as you
I don't think zero is a domain. Cuz range was >=1, it would reach close to zero but not zero as such.
Exactly zero was not the domain of f^-1(x) thats why it was 0<x<=-2.5 rather than 0<=x<=-2.5
I am disappointed for doing such a foolish mistake by by forgetting that 0 inequality and writing instead x<=-2.5.