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If \(x>1\), what is the value of the function \(y=|x-1|-|x+3|\)?यदि \(x>1\), तो फलन \(y=|x-1|-|x+3|\) का मान क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(y=-4\)\(y=-4\)
For \(x>1\), both \(x-1\) and \(x+3\) are positive. Hence, \(|x-1|=x-1\) and \(|x+3|=x+3\). Therefore, \(y=(x-1)-(x+3)=-4\). Option B results from ignoring the negative sign, while the correct value is the constant \(-4\) for every \(x>1\). Exam tip: Always determine the sign of each expression before removing modulus bars.जब \(x>1\), तब \(x-1>0\) और \(x+3>0\), इसलिए \(|x-1|=x-1\) तथा \(|x+3|=x+3\)। अतः \(y=(x-1)-(x+3)=-4\)। विकल्प B में ऋण चिह्न की उपेक्षा हो गई है, जबकि सही उत्तर सभी \(x>1\) के लिए स्थिर मान \(-4\) है। परीक्षा-युक्ति: मॉड्यूलस खोलने से पहले संबंधित व्यंजक का चिह्न अवश्य जाँचें।
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