Question

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

Answer 1

Given,

f: A → B and g: B → A satisfy g o f = I_A

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.