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JEE Main202125 Jul 2021Evening ShiftMathematicsFunctionsActual

Consider function f : A → B and g : B → C A , B , C ⊆ R such that g o f - 1 exists, then:

Options

  1. Af and g both are one-one
  2. Bf and g both are onto
  3. Cf is one-one and g is onto
  4. Df is onto and g is one-one

Correct answer

C. f is one-one and g is onto

Step-by-step solution

∴ g o f - 1 exist ⇒ g o f = g f x is bijective ⇒ f must be one-one and g must be onto.

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