Answer: f must be one-one, but g need not be.
- A Neither f nor g need be one-one
- B f must be one-one, but g need not be
- C g must be one-one, but f need not be
- D Both f and g must be one-one
Correct answer: B. f must be one-one, but g need not be
Explanation: If f(x₁) = f(x₂) then g(f(x₁)) = g(f(x₂)), forcing x₁ = x₂; g can still collapse points outside the range of f.
Concept context
Types of relations, equivalence classes, one-one and onto functions, composition, and invertible functions