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Prove that f is bijective - [Iran Second Round 1983]

Source:

December 30, 2010
functionalgebra proposedalgebra

Problem Statement

Let f,g:R→Rf, g : \mathbb R \to \mathbb R be two functions such that g∘f:R→Rg\circ f : \mathbb R \to \mathbb R is an injective function. Prove that ff is also injective.
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