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Choose the correct statement for (f:(1,\infty)\to\mathbb{R}), (f(x)=\frac{x+2}{x-1}).फलन (f:(1,\infty)\to\mathbb{R}), (f(x)=\frac{x+2}{x-1}) के लिए सही कथन चुनिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is one-oneयह एकैकी है
Step 1: (f'(x)=\frac{(x-1)-(x+2)}{(x-1)^2}=\frac{-3}{(x-1)^2}). Step 2: This is always negative for (x>1), so the function is strictly decreasing. Step 3: A strictly decreasing function is also one-one.चरण 1: (f'(x)=\frac{(x-1)-(x+2)}{(x-1)^2}=\frac{-3}{(x-1)^2}) है। चरण 2: यह (x>1) पर हमेशा ऋणात्मक है, इसलिए फलन सख्ती से घटता है। चरण 3: सख्ती से घटता हुआ फलन भी एकैकी होता है।
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