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If (f:A\to B) and (g:B\to C) are both onto functions, what can be said about (g\circ f)?यदि (f:A\to B) और (g:B\to C) दोनों आच्छादी फलन हैं, तो (g\circ f) कैसा होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It will be ontoआच्छादी होगा
Step 1: Take any (c\in C). Since (g) is onto, there is (b\in B) such that (g(b)=c). Step 2: Since (f) is onto, there is (a\in A) such that (f(a)=b), so (g(f(a))=c). Step 3: The composition of two onto functions is onto.चरण 1: (C) के किसी भी (c) को लें। (g) आच्छादी है, इसलिए कोई (b\in B) होगा जिससे (g(b)=c)। चरण 2: (f) आच्छादी है, इसलिए कोई (a\in A) होगा जिससे (f(a)=b)। तब (g(f(a))=c)। चरण 3: दो आच्छादी फलनों का संयोजन आच्छादी होता है।
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