Correct way of saying that some value depends on another value x only by a function of x I would like to know what good and valid ways there are to say (in words) that some value f(x), which depends on a variable x, in fact only depends on x "through" some function of x.
Example: For $x\in\mathbb{R}$ let $\hat{x}:=\min(0,x)$ and let f be a function such that $f(x)=f(\hat{x})$ for all x. I want to express that "f only depends on x 'through' $\hat{x}$".
How to formulate this (in words rather than writing it down in formulas)?
While for the above example it may be easier to just write down the formula, there can of course be more complex situations, in particular when not dealing with numbers, for example that the expectation of a random variable "depends on the r.v. only through its distribution".

Translating the formulas to words is one way: f is a function of x such that if we denote g(x) by y, f can be written as a function of y only. Perhaps not exactly what you are looking for.
