If functions f: A → B and g: B → A satisfy g o f = IA,

Question:

 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.

Solution:

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.

Hence, ‘g’ is also one-one and onto.

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