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Does there exist any continuous function f such that f(f(x))=-x^{2019}

Source: MTRP 2018 Class 11-Short Answer Type Question: Problem 3 :-

February 17, 2021

functionalgebra

Problem Statement

Does there exist any continuous function

f

such that

f(f(x))=-x^{2019}\ \forall\ x \in \mathbb{R}