Question
Download Solution PDFफलन y = cos-1 (x2 - 9) के प्रांत का पता लगाऐं।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
यदि cos-1 x = y है तो x = cos y
गणना:
जैसा कि हम जानते हैं कि,यदि cos-1 x = y है तो x = cos y
इस प्रकार,y = cos-1 (x2 - 9) --------(दिया गया है)
⇒ x2 - 9 = cos y
जैसा कि हम जानते हैं , -1 ≤ cos y ≤ 1, जहाँ y ∈ R
⇒ - 1 ≤ x2 - 9 ≤ 1
असमिका के सभी पक्षों में 9 जोड़ने पर ,हमें मिलता है
⇒ 8 ≤ x2 ≤ 10
उपरोक्त असमिका को निम्न रुप से पुनःलिखने पर
⇒ 2√2 ≤ |x| ≤ √10
⇒ x ∈ [-√10, -2√2] ∪ [2√2, √10]
अतः,दिए गए फलन का प्रांत [-√10, -2√2] ∪ [2√2, √10] है।
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