Great study! The functional role of the Father is to be a Father to the Fatherless. To show us by His example how to be a good Father. Many have no earthly father role model in their life. So many broken homes. In the Godhead, the Heavenly Father is our disciplinarian.

Heb 12:9 Furthermore we have had fathers of our flesh which corrected us, and we gave them reverence: shall we not much rather be in subjection unto the Father of spirits, and live?

In the verses prior and after we see the role of the Heavenly Father to correct, show us by His correction we a legitimate and to mature us to be patakers of His holiness!
Great and needful study as the false religions and Jesus cults, most all have a problem with the Trinity. Either only one God, the Oneness Group or polytheist like the LDS.
Thanks and God bless!