Incorrect results and quirks

[Bill_G]

My opinion on your question is a bit mathematical:

The function F1(X) is a multivalued function (i.e. 1/3 power) that has singularities at X=2 and X=-2, which are commonly called Branch Points.

Your function has 3 branches (i.e., that is to properly plot F1(X) you need 3 graphs with a Branch Cut between -2 to 2) and to completely analyze it you need to consider the function in terms of complex variable Z. HP Prime does not do this unless you write a program to do it.

Your first plot of F1(X) is corrrect in the the First Branch of the function, since for magnitude of X<2 in enters another branch.

The plot of F1(X) using NTHROOT seem to be combining the answer from two branches, since the HELP says that NTHROOT returns the primary root value (which is real in F1(X). So it is also evaluating the function for magnitude of X<2, but that part of the graph is really in another branch..

I had these things happening with multivalued function.