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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 24 (2000), Issue 3, Pages 213-216
doi:10.1155/S0161171200003847

Composition of functions

Kandasamy Muthuvel

Department of Mathematics, University of Wisconsin Oshkosh, Oshkosh 54901-8601, Wisconsin, USA

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.