f(f(x)) = exp(x) - x
what is f(x) ?
does the (only) fixpoint at - oo help ?
can f(x) be entire ?
is there a solution f(x) such that f(x) has no fixpoint apart from - oo ?
can f(x) be expressed in terms of tetration ?
is there a solution f(f(x)) = exp(x) - x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo ?
does " a solution f(f(x)) = exp(x) - x with f(x) E Coo , f(x) mapping all reals to reals and f(x) having no fixpoint apart from - oo " imply that all derivatives are strictly positive reals ?
can f(x) be expressed in terms of pentation ?
does the substitution y = 1/x help ?
( trying to 'move the fixpoint' but problems occur e.g. exp(1/x) has a singularity at 0 ! )
this seems like a difficult problem ...
regards
tommy1729
stop looking at monty hall and inaccessible cardinals and take a look at this.
surely questions of tommy1729 must be trivial hmm
this is your glorious moment to show my questions are trivial and/or you are brilliant.
I MEANT f(f(x)) = exp(x) + x !!
tommy1729