How do you define symmetry of a multidimensional function?

Question

Let $f:\mathbb{R} \rightarrow \mathbb{R}$. Then $f$ is symmetric if $f(x)=f(-x)$. How do you define symmetry for the function $f:\mathbb{R}^n \rightarrow \mathbb{R}$? for $f:\mathbb{R}^n \rightarrow \mathbb{R}^d$?

Answer 1

Exactly the same way: $f$ is symmetric if $f(x) = f(-x)$, where if $x = (x_1, ..., x_n) \in \mathbb{R}^n$, $-x = (-x_1, ..., -x_n)$.