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On (\mathbb{R}), (a*b=a+b+5). What is the inverse of (a)?(\mathbb{R}) पर (a*b=a+b+5) है। (a) का प्रतिलोम क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (-a-10)(-a-10)
Step 1: First find the identity (e): (a+e+5=a), so (e=-5). Step 2: For inverse (b), use (a+b+5=-5). Step 3: Hence (b=-a-10); inverse is always found with respect to the identity element.चरण 1: पहले तत्समक अवयव (e) निकालें, (a+e+5=a), इसलिए (e=-5)। चरण 2: प्रतिलोम (b) के लिए (a+b+5=-5)। चरण 3: (b=-a-10); प्रतिलोम हमेशा तत्समक अवयव के सापेक्ष निकाला जाता है।
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