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If (f:\mathbb{R}\setminus{2}\to\mathbb{R}), (f(x)=\frac{x^2-4}{x-2}), what is the correct conclusion about the one-one nature of (f)?यदि (f:\mathbb{R}\setminus{2}\to\mathbb{R}), (f(x)=\frac{x^2-4}{x-2}), तो (f) की एकैकीता पर सही निष्कर्ष क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneएकैकी है
Step 1: For (x\neq 2), (\frac{x^2-4}{x-2}=x+2). Step 2: In (x+2), the coefficient of (x) is non-zero, so equal images give equal inputs. Step 3: While simplifying, keep the removed point outside the domain.चरण 1: (x\neq 2) पर (\frac{x^2-4}{x-2}=x+2) हो जाता है। चरण 2: (x+2) में (x) का गुणांक शून्य नहीं है, इसलिए समान छवि से समान आगत मिलेगा। चरण 3: सरलीकरण करते समय हटाए गए बिंदु को क्षेत्र से बाहर ही रखें।
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