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On the set (\mathbb{R}\setminus{-1}), (a*b=a+b+ab) is defined. What is the inverse of (a)?समुच्चय (\mathbb{R}\setminus{-1}) पर (a*b=a+b+ab) परिभाषित है। (a) का प्रतिलोम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{-a}{1+a})(\frac{-a}{1+a})
Step 1: First find the identity; from (a*e=a), (e=0). Step 2: For inverse (b), use (a*b=0), so (a+b+ab=0). Step 3: (b(1+a)=-a), hence (b=\frac{-a}{1+a}); always confirm the identity before finding inverse.चरण 1: पहले तत्समक अवयव निकालें, (a*e=a) से (e=0)। चरण 2: प्रतिलोम (b) के लिए (a*b=0), इसलिए (a+b+ab=0)। चरण 3: (b(1+a)=-a), अतः (b=\frac{-a}{1+a}); प्रतिलोम में पहले तत्समक अवयव पक्का करें।
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