Expanding composite function one in terms of the other in a power series

Question

if I have a composite function $\rho(V(x))$, is it possible to write $\rho$ in a power series as follows, $$\rho(V(x)) \sim a_{0} + a_{1}V(x) + a_{2}(V(x))^{2} +.... +a_{n}(V(x))^{n}$$. Is this correct , Does this make sense and mathematically correct in any way? In short , I want to express $\rho$ as a function of $V$ in a power series. Please also provide some reference if there is any. I am from physics background sorry if my question looks utterly wrong.