Frivolous means lacking seriousness or sense. Foolish means showing lack of good sense or judgment. Both suggest silliness or lack of seriousness, so they are synonyms.
Frugality means the quality of being economical with resources. Thrift means careful management of money or resources. Both describe saving and avoiding waste, hence synonyms.
Frustration means the feeling of being upset due to failure. Thwarting means preventing someone from accomplishing something. Both relate to blocking success, so they are synonyms.
Functionary means a person who performs official duties. An official is a person holding a position of authority or duty. Both describe someone serving in an official role, so they are synonyms.
Futility means pointlessness or ineffectiveness. Uselessness means having no practical purpose. Both mean lacking effectiveness, so they are synonyms.