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continous onto function

Source: Romanian Nationals RMO 2005 - grade 11, problem 2

March 31, 2005
functiontrigonometryalgebradomainlimitreal analysisreal analysis solved

Problem Statement

Let f:[0,1)→(0,1)f:[0,1)\to (0,1) a continous onto (surjective) function. a) Prove that, for all a∈(0,1)a\in(0,1), the function fa:(a,1)→(0,1)f_a:(a,1)\to (0,1), given by fa(x)=f(x)f_a(x) = f(x), for all x∈(a,1)x\in(a,1) is onto; b) Give an example of such a function.
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