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If (f:A\to B) and (g:B\to A) satisfy (g\circ f=I_A), what conclusion about (f) is definitely true?यदि (f:A\to B) और (g:B\to A) इस प्रकार हैं कि (g\circ f=I_A), तो (f) के बारे में कौन सा निष्कर्ष निश्चित है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f) is one-one(f) एकैकी है
Step 1: Suppose (f(a_1)=f(a_2)). Step 2: Applying (g) to both sides gives (g(f(a_1))=g(f(a_2))), so (a_1=a_2). Step 3: If a left inverse exists, the original function is one-one.चरण 1: मान लें (f(a_1)=f(a_2))। चरण 2: दोनों ओर (g) लगाने पर (g(f(a_1))=g(f(a_2))), अर्थात (a_1=a_2)। चरण 3: यदि बायाँ व्युत्क्रम मौजूद हो, तो मूल फलन एकैकी होता है।
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