Question
Download Solution PDFफलन f(x) = sin-1 (x + 1) का डोमेन क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
sin-1 x का डोमेन [-1, 1] है
एक असमानता के दोनों पक्षों से समान राशि को जोड़ने या घटाने पर अपरिवर्तित असमान चिन्ह छोड़ता है।
गणना:
दिया गया है: f(x) = sin-1 (x + 1)
चूँकि हम जानते हैं, sin1 x का डोमेन [-1, 1] है
इसलिए, -1 ≤ (x + 1) ≤ 1
उपरोक्त असमानता में 1 को घटाने पर,
⇒ -1 - 1 ≤ x + 1 - 1 ≤ 1 - 1
⇒ -2 ≤ x ≤ 0
∴ sin-1 (x + 1) का डोमेन [-2, 0] है
Mistake Points[-2, 0] [-2, 0] से अलग है। '[' and ']' इंगित करता है कि अंतिम संख्या (2 और 0) भी शामिल है। '(' and ')' इंगित करता है कि 2 और 0 को ध्यान में नहीं रखा गया है।
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