Mathematics

The key insight here is understanding what "always true" means—you need a property that holds for every function, regardless of its specific form or domain/codomain. Think about the fundamental definitions: what must be true just from the fact that $f$ is a function? Consider whether properties like injectivity, surjectivity, or continuity are guaranteed, or whether they depend on the specific function. The answer lies in what the definition of a function itself requires, not in special cases.

The key insight here is understanding what "always true" means—you need a property that holds for every function, regardless of its specific form or domain/codomain. Think about the fundamental definitions: what must be true just from the fact that $f$ is a function? Consider whether properties like injectivity, surjectivity, or continuity are guaranteed, or whether they depend on the specific function. The answer lies in what the definition of a function itself requires, not in special cases.