Does there exist functions such that and for all real numbers
a) if ?
b) if ?
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Does there exist functions $f,g: \mathbb{R}\to\mathbb{R}$ such that $f(g(x)) = x^2$ and $g(f(x)) = x^k$ for all real numbers $x$
a) if $k = 3$?
b) if $k = 4$?
Izvor: Međunarodna matematička olimpijada, shortlist 1997
Školjka 
such that 
and 
for all real numbers 
? 
?