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The monotonic function u(x)

Source: Romanian TST 1998

April 23, 2011
functionalgebra proposedalgebrafunctional equation

Problem Statement

Find all monotonic functions u:R→Ru:\mathbb{R}\rightarrow\mathbb{R} which have the property that there exists a strictly monotonic function f:R→Rf:\mathbb{R}\rightarrow\mathbb{R} such that f(x+y)=f(x)u(x)+f(y)f(x+y)=f(x)u(x)+f(y) for all x,y∈Rx,y\in\mathbb{R}.
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