International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 213-216
doi:10.1155/S0161171200003847
Composition of functions
Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh 54901-8601, Wisconsin, USA
Received 26 March 1999; Revised 11 August 1999
Copyright © 2000 Kandasamy Muthuvel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We prove that if f and g are functions from the reals into
the reals such that the composition of g with f is continuous
and f is both Darboux and surjective, then g is continuous. We
also prove that continuous and Darboux can be interchanged in the
above statement.