If functions f: A → B and g: B → A satisfy g o f

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

Harshit Singh · Accepted Answer

Dear StudentGiven,f: A &rarr; B and g: B &rarr; A satisfy g o f = IAIt&rsquo;s clearly seen that function &lsquo;g&rsquo; is inverse of &lsquo;f&rsquo;. So, &lsquo;f&rsquo; has to be one-one and onto.Thus, &lsquo;g&rsquo; is also one-one and onto.Thanks

Analytical Geometry> If functions f: A → B and g: B → A satisf...

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

Pawan Prajapati , 4 Years ago

Harshit Singh

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Analytical Geometry> If functions f: A → B and g: B → A satisf...

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

Pawan Prajapati , 4 Years ago

Harshit Singh

Provide a better Answer & Earn Cool Goodies

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