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Function preserving triangle inequality

Source: China Team Selection Test 2016 Test 3 Day 2 Q6

March 26, 2016
algebrafunction

Problem Statement

Find all functions f:R+ā†’R+f: \mathbb R^+ \rightarrow \mathbb R^+ satisfying the following condition: for any three distinct real numbers a,b,ca,b,c, a triangle can be formed with side lengths a,b,ca,b,c, if and only if a triangle can be formed with side lengths f(a),f(b),f(c)f(a),f(b),f(c).
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