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On (\mathbb{R}\setminus{-1}), for (a*b=a+b+ab), what is the inverse of (a)?समुच्चय (\mathbb{R}\setminus{-1}) पर (a*b=a+b+ab) के अंतर्गत (a) का प्रतिलोम क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (\frac{-a}{1+a})(\frac{-a}{1+a})
Step 1: The identity is (0). Step 2: For inverse (b), (a*b=0), so (a+b+ab=0). Thus (b(1+a)=-a), giving (b=\frac{-a}{1+a}). Step 3: To find inverse, set (a*b=e).चरण 1: पिछले विचार से तत्समक (0) है। चरण 2: प्रतिलोम (b) के लिए (a*b=0), यानी (a+b+ab=0)। इससे (b(1+a)=-a), इसलिए (b=\frac{-a}{1+a})। चरण 3: प्रतिलोम निकालते समय हमेशा (a*b=e) लिखें।
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