Problem 13

Due in DSC 203 by 3 PM, Friday April 13, 2001

Assume that $f,g:{\mathbb R}\longrightarrow{\mathbb R}$ are continuous functions such that f(g(x))=g(f(x)) for all x. Suppose that there is a real number x₀ such that f(f(x₀))=g(g(x₀)). Show that then the equation f(x)=g(x) has a solution.

Solutions, questions and/or comments should be directed to Judy Downey or Griff Elder

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Last modified:   Mon Apr 2 20:18:37 CDT 2001