Re: " f o f = g ; f a half effect of g "

alainverghote@xxxxxxxx nous a récemment amicalement signifié :

I do neither search all the solutions nor discuss at length
the intervals where the given functions are defined,


You MUST discuss intervals where the functions are defined and the property verified.

Else (example already given on fr.sci.maths) :

f(x) = -x for x > +1
f(x) = g(-x) for x < -1
f(x) = (1 + g(-1))(1 - x)/2 - 1 for x in [-1, 1]

f is a continuous function defined on R and fof = g for every x in [1, +oo[

--
Patrick

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