I have a standard state-space representation of a nonlinear system
$$\dot{\vec{x}}(t) = \vec{f}(\vec{x}(t), u(t))$$
Expanded, this non-linear relationship looks like
$$\dot{\vec{x}}(t) = \begin{bmatrix} \dot{a}(t)\\\dot{b}(t)\\\dot{c}(t) \end{bmatrix} = \begin{bmatrix} f_1(a(t), \mu(t))\\ f_2(b(t), c(t), \gamma(t))\\ f_3(b(t), c(t), \gamma(t)) \end{bmatrix} $$
And there's some supporting functions
\begin{align} \mu(t) &= f_4(u(t)) \\ \gamma(t) &= f_5(\mu(t), a(t), b(t), c(t))\end{align}
Question: How do I write that all functions $f_1$ to $f_5$ make up function $f$?
With union? Something like $f = f_1 \cup f_2 \cup\cdots \cup f_5$?
I also saw something like $f=\bigcup\{f_i:i\in\{1,2,\cdots, 5\}\}$
(Or is this not required?)