Answer: f⁻¹ must be defined at every element of the codomain, which requires each to have a preimage.
- A The inverse is only defined for continuous functions in most cases
- B f⁻¹ must be defined at every element of the codomain, which requires each to have a preimage
- C One-one functions never possess inverses in standard practice
- D Ontoness alone is sufficient for invertibility without injectivity
Correct answer: B. f⁻¹ must be defined at every element of the codomain, which requires each to have a preimage
Explanation: f⁻¹ : B → A must assign a value to every b ∈ B; if some b has no preimage the inverse is undefined there.
Concept context
Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions