Solution
= Solution
\b[False.] Compositions of scalings $z\mapsto\mu z$ and inversion $z\mapsto1/z$ reduce to one of the forms $\nu z$ or $\nu/z$; they preserve the unordered pair $\{0,\infty\}$. But
$$
f(z)=\frac{z}{z+1}
$$
is a <Möbius transformation> fixing $0$ and sends infinity to $1$, so it cannot be such a composition.