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If functions f: A → B and g: B → A satisfy g o f = IA, then show that f is one-one and g is onto

 If functions f: A → B and g: B → A satisfy g o f = IA, then show that f is one-one and g is onto

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
3 years ago
Dear Student

Given,
f: A → B and g: B → A satisfy g o f = IA
It’s clearly seen that function ‘g’ is inverse of ‘f’. So, ‘f’ has to be one-one and onto.
Thus, ‘g’ is also one-one and onto.

Thanks

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