Consider a vector $\pmb{v}=(v_1, v_2...,v_n) \in \mathbb{R}^n$ and a function $f: \mathbb{R} \to \mathbb{R} $. What is the best way to denote the vector $(f(v_1), f(v_2)....,f(v_n))$?
Writing $f(\pmb{v})$ isn't exactly correct as $f$ is not $\mathbb{R}^n \to \mathbb{R}^n$.
Edit: Based on comment below - imagine dimension of $\pmb{v}$ here is not known ahead of time.
You can handle this many ways. There is no consistent notation for this. Books and many programming lanuages handle it differently.
You pointed with $f(v)$ already a nice way out. It is just important to be clear on the notation, that means if it is not 100% obvious in the context define it that way.