For what values of a does lim_x-->a f(x) exist

[karush]

View attachment 1664

Basically I am trying to understand this question,

the graph is $$\lim_{x to a} {([[x]]+[[-x]])}$$

the last \(\displaystyle 2\) lines are the answers from W|A.

First, is looks like an greatest integer function, or notated as the floor function
next I presume \(\displaystyle \displaystyle x\rightarrow\text{a}\) is where on the \(\displaystyle x\) axis where the limit exists
it appears just from the graph that there are holes at the integer values
but not sure what the imaginary part means?

 

[Ackbach]

The W/A plot is missing some important details. I would try plotting $ \lfloor x \rfloor$ and $\lfloor -x \rfloor$ separately, by hand. Then plot the sum $\lfloor x \rfloor+ \lfloor -x \rfloor$ by hand. Pay particular attention to integer values of $x$, and what happens to them.