Thinking hard about easy content: Odd and even functions

When asked to define an even function, a student wrote: “A function f for which f(−x) = f(x).” Is this OK? It’s quite a good answer – the idea is clearly right. But I would have liked the student to have written something like “for all values of x”, or “for all values of x in the domain of f”. Am I being too fussy? If the student had used the identity symbol (see Foster, 2021) to express this as f(−x) ≡ f(x), then I would have been satisfied. But, as it stands, f(−x) = f(x) could express something that is true for only certain values of x. How might I address this without seeming to be annoyingly pernickety?