What is the return type of a multi-valued function?

Question

The most commonly used definition is as follows: "A multifunction is a mapping between $D$ and $\mathcal{P}(E)$, where $D$ and $E$ are some sets." However, the following notations are commonly used: $f(1)=2$ (where $f: \mathbb{R}\rightarrow\mathbb{R}$, and, for example, $f(1)$ is $\{1, 2, 3\}$), $f(1)+3=5$, and so on.
If $f$ returns a subset of reals, wouldn't that imply that, technically, $\{1, 2, 3\}=2$? So the operator $=$ is defined differently if the types on the left- and right-hand sides differ?
Or maybe $f$ returns not a set, but a more complex structure, something like a tuple?