Name of a function that can not be described by a lower-dimensional function

I am looking for a good name of a function $f:\mathbb{R}^n\to \mathbb{R}$ satisfying the following property:

There does not exist function $g:\mathbb{R}^k\to \mathbb{R}$, $k<n$, such that $f(\textbf{x}) = g(\tilde{\textbf{x}}) $ for almost all $ \textbf{x}\in\mathbb{R}^n, \tilde{\textbf{x}}\in\mathbb{R}^k$. Here, almost all means that the inequality can hold on a Lebesgue measure zero.

Is there some related notion in the literature? I suggest something like 'not full ranked' or 'not full dimension', but these notions have different definitions in the literature.