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If \(f:\mathbb{R}\to\mathbb{R}\) and \(f(x)=|x+1|+|x-1|\), is (f) one-one?यदि \(f:\mathbb{R}\to\mathbb{R}\) तथा \(f(x)=|x+1|+|x-1|\) है, तो (f) एक-एक है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Noनहीं
Step 1: On \(-1\le x\le1\), this sum becomes constant. Step 2: For example \(f(0)=2\) and \(f\left(\frac{1}{2}\right)=2\), while \(0\neq \frac{1}{2}\). Step 3: In sums of absolute values look for constant intervals.चरण 1: \(-1\le x\le1\) पर यह योग स्थिर हो जाता है। चरण 2: उदाहरण के लिए \(f(0)=2\) और \(f\left(\frac{1}{2}\right)=2\), जबकि \(0\neq \frac{1}{2}\)। चरण 3: निरपेक्ष मानों के योग में स्थिर भाग खोजें।
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