\(|f\inv(3)| \le 1\text{.}\) In other words, either \(f\inv(3)\) is the empty set or is a set containing exactly one element. Injective functions cannot have two elements from the domain both map to 3.
\(|f\inv(3)| \ge 1\text{.}\) In other words, \(f\inv(3)\) is a set containing at least one elements, possibly more. Surjective functions must have something map to 3.
\(|f\inv(3)| = 1\text{.}\) There is exactly one element from \(X\) which gets mapped to 3, so \(f\inv(3)\) is the set containing that one element.