​ Consider function f : A → B and g : B → C (A, B, C ⊆ R) such that (gof)^–1 exists, then: (1) f and g both are one-one (2) f and g both are onto

Question

Consider function f : A → B and g : B → C (A, B, C \(\subseteq\) R) such that (gof)^–1 exists, then:

(1) f and g both are one-one

(2) f and g both are onto

(3) f is one-one and g is onto

(4) f is onto and g is one-one

Answer 1

Answer is: (3) f is one-one and g is onto

∴ (gof)^–1 exist ⇒ gof is bijective

⇒ ‘ƒ’ must be one-one and ‘g’ must be ONTO