/sci/ - Science & Math

>>15044451
i am trying to prove this is injective but i'm stuck because i cant tell if g and h are injective, or even if this matters.

i have for f(x) = f(y)
xog = yog & xoh = yoh
am i allowed to remove g (like subtracting it from both sides) and do
x=y

or do i have to get rid of g by complementing xog with its inverse (which i dont know if it has), where gog^-1 is the identity function?