The question is “Prove that the limit as x approaches zero of f(x)=the limit as x approaches a of f(x-a).
I have taken a few stabs at the problem and was told that the solution was the image I attached.
The given proof largely makes sense to me, only it seems to be a proof that the limit as x approaches a of f(x) equals the limit as y approaches zero of g(y-a). I don’t see how this is a proof of what was asked, and I also don’t see how to proceed in the other direction. I think my issue is that I’m struggling to connect my intuitive/verbal understanding with epsilon-delta limit notation, and changing the variable from x to y also confuses me. Can anyone help make sense of this?