MathDB

all f s.t. (f²)'=f

Source: Romanian National Olympiad 2016, grade xi, p.1

August 25, 2019

real analysisFind all functionsdifferentiabilityDarbouxfunction

Problem Statement

Find all functions,

f:\mathbb{R}\longrightarrow\mathbb{R} ,

that have the properties that

f^2

is differentiable and

f=\left( f^2 \right)' .