RMM 2013 Problem 2 Day 1 Does there exist a pair (g,h)(g, h)(g,h) of functions g,h:R→Rg, h: \mathbb{R} \rightarrow \mathbb{R}g,h:R→R such that the only function f:R→Rf: \mathbb{R} \rightarrow \mathbb{R}f:R→R satisfying f(g(x))=g(f(x))f(g(x))=g(f(x))f(g(x))=g(f(x)) and f(h(x))=h(f(x))f(h(x))=h(f(x))f(h(x))=h(f(x)) for all x∈Rx \in \mathbb{R}x∈R is the identity function f(x)≡xf(x) \equiv xf(x)≡x ? (United Kingdom) Alexander Betts Dataset text NuminaMath olympiads. Quoted with source. Solutions No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label. Add a solution PreviousProblem 1 NextProblem 3 Locator rmm/2013/p2 · Tag VVZT2G9QGQ · Edit this page on GitHub · Keys: j next, k previous