The question asks to identify the Rastrakuta king who authored or patronized the work 'Kavirajamarga'.
'Kavirajamarga' is a significant literary work in Kannada. It is widely attributed to the patronage and influence of the Rastrakuta king Amoghavarsha I, also known as Nripatunga.
While the exact authorship is debated, with some sources suggesting Court Poet Sri Vijaya wrote it under Amoghavarsha's guidance, the work is strongly associated with Amoghavarsha's reign and name (Nripatunga). Therefore, Amoghavarsha is considered the correct answer in the context of the question.
Correct Option: C