MathDB

Composition of off functions (archivation post)

Source:

October 8, 2018

function

Problem Statement

Let

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

be functions with the property that f\left( g(x) \right) =g\left( f(x) \right) =-x, \forall x\in\mathbb{R}
a) Show that

f,g

are odd. b) Give a concrete example of such

f,g.