I have a very very basic question on CDF and limits

[Roni1985]

I am taking an "introduction to probability" class and there is a question (related to calculus) that the professor is not going to go over it.

Here is the question:

1. For a random variable X, the function F defined by
F(x) = P(X <= x),−inf < x < inf
is called the cumulative distribution function of X. A property of every distribution function F is that
it is right continuous with left limits.
For the following functions, determine if they are right continuous and/or have left limits at the
indicated values. (A “yes” or “no” answer is insufficient. Justify your answers or no credit will be
given.)
(a) at x = 0 and x = 1 for G(x) = |x|/x .
(b) at x = 0 and x = 1 for H(x) = arctan(x).

Well, if we look at 'a', I was trying to find the limit when x->0+ and limit when x->0-. I am getting -1 and 1
but the function is not defined at x=0.
and it's not right continuous nor left continuous, and it has right and left limits, correct?

OR I don't get the question.

Can somebody tell me what I need to do here or lead me to the correct way ??

Thanks in advance,
Roni.

 

[Roni1985]

ops, didn't see you have a homework forum :/