International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 213-216

Composition of functions

Kandasamy Muthuvel

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.


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.