Difference between revisions of "1973 IMO Problems/Problem 5"
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Revision as of 18:42, 25 October 2014
is a set of non-constant functions of the real variable
of the form
and
has the following properties:
(a) If and
are in
, then
is in
; here
.
(b) If is in
, then its inverse
is in
; here the inverse of
is
.
(c) For every in
, there exists a real number
such that
.
Prove that there exists a real number such that
for all
in
.