Question
Download Solution PDFफलन y = cos-1 (x2 - 4) का डोमेन ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFधारणा:
यदि cos-1 x = y तो x = cos y
गणना:
जैसा कि हम जानते हैं कि यदि cos-1 x = y तो x = cos y
तो y = cos-1 (x2 - 4) --------(दिया हुआ)
⇒ x2 - 4 = cos y
जैसा कि हम जानते हैं कि, -1 ≤ cos y ≤ 1, जहाँ y ∈ R
⇒ - 1 ≤ x2 - 4 ≤ 1
असमीकरण के सभी पक्षों पर 4 जोड़कर हमें मिलता है
⇒ 3 ≤ x2 ≤ 5
हम उपरोक्त असमीकरण को फिर से निम्न रूप में लिख सकते हैं
⇒ √3 ≤ |x| ≤ √5
⇒ x ∈ [-√5, -√3] ∪ [√3, √5]
इसलिए दिए गए फलन का डोमेन [-√5, -√3] ∪ [√3, √5] है
Last updated on Jun 30, 2025
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