Is
identically zero at x=0, or does it have a singularity?
EDIT: silly me. I didn't mean to write 'z' there, just been doing too much complex analysis recently and got into the habit of writing z everywhere.
Sorry for the confusion!
The function is not defined at x = 0. There is a singularity at x = 0. However, exists and is equal to zero (as previously shown). The point x = 0 is therefore a removable singularity (often called a 'hole').
The function can therefore be 'fixed' if it is defined as
in which case you can now say that f(0) = 0.