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  • If functions f: A → B and g: B → A satisfies g of = IA, then show that f is one-one and g is onto.

If functions f: A \rightarrow B \: \: and\: \: g: B \rightarrow A \text{ satisfies } g of = IA, then show that f is one-one and g is onto.

Answers (1)

Here, it is given:

f: A \rightarrow B \: \: and\: \: g: B \rightarrow A \text{ satisfies } g of = IA

It’s clear here that the function ‘g’ is inverse of ‘f’.

So, ‘f’ has to be both one-one as well as onto.

As a result, ‘g’ is both one-one and onto.

Posted by

infoexpert22

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