f:R⟶R+ is a non-decreasing function. Prove that there is a point a∈R that f(a+1f(a))<2f(a)
Problem
Source: Iranian National Olympiad (3rd Round) 2002
Tags: function, limit, algebra proposed, algebra
Source: Iranian National Olympiad (3rd Round) 2002
Tags: function, limit, algebra proposed, algebra
f:R⟶R+ is a non-decreasing function. Prove that there is a point a∈R that f(a+1f(a))<2f(a)