I'm talking about $f: X \rightarrow Y$ where $X$ is a stand-in for the function's inputs and $Y$ is a stand-in for the function's outputs. One example from one of my college classes was $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$. Cryptography is filled with this notation like $\mathcal{E}: \mathcal{K} \times \mathcal{M} \rightarrow \mathcal{C}$ and $H: \{0, 1\}^{k} \times \{0, 1\}^{*} \rightarrow \{0, 1\}^{h}$. My question is the same as the title.
Furthermore, how can it known from this description which element of $X$ corresponds to which parameter of $f$ when $f$ is written with the parentheses its arguments? You could go by the order in which the elements in $X$ are listed, but this leaves ambiguous the argument name each element corresponds to, so I decided to write it like $F(x, y): \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$, $G(x, y): \mathbb{R}^{2} \rightarrow \mathbb{R}$, and $H(K, X): \{0, 1\}^{k} \times \{0, 1\}^{*} \rightarrow \{0, 1\}^{h}$.