Grade 12Analytical Geometry
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
1 Answer
Harshit Singh
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
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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