CatalinBordea wrote: Find all derivable functions that have real domain and codomain, and are equal to their second functional power. When you translate a problem, you should try to reproduce as well as possible the original wording rather than adapting it. I'm not sure whether "second functional power" makes sense or not. Here is a closer form: Quote: Find the differentiable functions $f: \mathbb{R} \to \mathbb{R}$ which fulfill the condition $f \circ f =f.$ Original paper: https://static.olimpiade.ro/uploads/attach_data/1/4/18//2014_matematica_nationala_clasa_a_xia_subiectebarem.pdf.

Filipjack wrote: CatalinBordea wrote: Find all derivable functions that have real domain and codomain, and are equal to their second functional power. When you translate a problem, you should try to reproduce as well as possible the original wording rather than adapting it. I'm not sure whether "second functional power" makes sense or not. Here is a closer form: Quote: Find the differentiable functions $f: \mathbb{R} \to \mathbb{R}$ which fulfill the condition $f \circ f =f.$ Original paper: https://static.olimpiade.ro/uploads/attach_data/1/4/18//2014_matematica_nationala_clasa_a_xia_subiectebarem.pdf. If I wouldn't adapt the spelling, some problems (not referring to this one, in particular) wouldn't make sense in English, or it would mean another thing than what's intended. Also, this is a univeristy-level forum where functional powers should be well known.(https://en.wikipedia.org/wiki/Function_composition#Functional_powers)