Clarification of the notation $f: \mathbb{R} \setminus\{3\} \to\mathbb{R}\setminus\{2\}$

Question

I have a question that uses the following notation: the function $f: \mathbb{R} \setminus\{3\} \to\mathbb{R}\setminus\{2\}$ is defined by $$f(x)=\frac{2x-3}{x-3}.$$

I understand that the left side specifies the domain of the function, and the right side specifies the codomain of the function.

However, the notations "${}\setminus\{3\}$" and "${}\setminus\{3\}$" seem to me confusing.

Any help in clarifying this would be greatly appreciated.

Answer 1

Every real number except $3$, every real number except $2$? This operation is set subtraction (subtract the set $\{3\}$ from the set of real numbers).

Answer 2

This is a set-minus sign (try reading here about it) between $\mathbb{R}$ and $\{2\}$ in $\mathbb{R}\setminus\{2\}$.