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Find two functions $f,g:\Bbb R\to \Bbb R$ that are not constant such that their composition is constant?

Any help, please. Can these functions be found?

EDIT: I try next, let $f:\Bbb R\to\Bbb R$ define $f(x)=1$ if $x\in\Bbb Q$ and $f(x)=-1$ if $x\in\Bbb R-\Bbb Q$ and $g:\Bbb R\to\Bbb R$ define by $g(x)=|x|$. Then $g\circ f=1$. Is good my try?

Andrew Madison
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1 Answers1

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Hint: what happens if you try to make $f,g$ as close to constant as possible i.e. $f(x_0)=C_0$ and $f(x)=C_1$ for all $x\neq x_0$?

A.M.
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