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Let $G$ be any group of functions. Let $H$ be the group of all compositions of functions of the form $f(mx)/m$ where $m>0$ and $f\in G$. Then $H$ is a group of the sort you're looking for, and all such groups arise in this way.
Let $G$ be any group of functions. Let $H$ be the group of functions of the form $f(mx)/m$ where $m>0$ and $f\in G$. Then $H$ is a group of the sort you're looking for, and all such groups arise in this way.
Let $G$ be any group of functions. Let $H$ be the group of all compositions of functions of the form $f(mx)/m$ where $m>0$ and $f\in G$. Then $H$ is a group of the sort you're looking for, and all such groups arise in this way.
Let $G$ be any group of functions. Let $H$ be the group of functions of the form $f(mx)/m$ where $m>0$ and $f\in G$. Then $H$ is a group of the sort you're looking for, and all such groups arise in this way.
