It depends on whether and are continuous at and respectively, and if you are allowed to use the result that if is continuous at .
If so, your reasoning is fine.
If not, you will need to use an proof.
Hey all, thanks again for all help in the past! Here's a limit question that I am unsure if I am overthinking, or if it's as simple as it looks.
lim f(x) as x-->a is equal to lim f(a+h) as h-->0 (this is really just an exercise in understanding what the terms are)
Now the easiest way would just to pop in the values and boom, lim f(a) = lim f(a). But I think he is looking for a different reasoning. My attempt was to kind of define the statements like so:
LHS: f can be made to be as close to a limit L as desired by making x sufficiently close to a.
RHS: f can be made to be as close to a limit L as desired by making h sufficiently close to zero.
And in this example, it just so happens when h is made to go to zero we are left with the respective equations L's equal to each other.
I don't think I've really "proved" anything though, have I?