Question
Download Solution PDFफलन \({\rm{f}}\left( {\rm{x}} \right) = \frac{1}{{\sqrt {\left| {\rm{x}} \right| - {\rm{x}}} }}\) का डोमेन क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
डोमेन: फलन f(x) के डोमेन को x के मान के रूप में परिभाषित किया जाता है जिसके लिए फलन f(x) मौजूद है।
\({\rm{f}}\left( {\rm{x}} \right) = \left| {\rm{x}} \right| = {\rm{\;}}\left\{ {\begin{array}{*{20}{c}} { - x,\;\;x < 0}\\ {x,\;\;x \ge 0} \end{array}} \right.\)
गणना:
हमें फलन \({\rm{f}}\left( {\rm{x}} \right) = \frac{1}{{\sqrt {\left| {\rm{x}} \right| - {\rm{x}}} }}\) का डोमेन ज्ञात करना है।
हम जानते हैं कि वर्गमूल सदैव धनात्मक होता है।
इसलिए, |x| - x > 0 (|x| - x ≠ 0)
⇒ |x| > x
चूँकि हम देख सकते हैं कि |x|, (-∞, 0) में x से बड़ा है।
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