Question
Download Solution PDFफलन f(x) = cos-1 (x - 2) का डोमेन क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
cos-1 x का डोमेन [-1, 1] है।
एक असमानता के दोनों पक्षों से समान मात्रा को जोड़ने या घटाने पर असमानता चिन्ह अपरिवर्तित रहता है।
गणना:
दिया गया है: f(x) = cos-1 (x - 2)
चूँकि हम जानते हैं, cos-1 x का डोमेन [-1, 1] है।
इसलिए, -1 ≤ (x - 2) ≤ 1
उपरोक्त असमानता में 2 जोड़ने पर,
⇒ -1 + 2 ≤ x - 2 + 2 ≤ 1 + 2
⇒ 1 ≤ x ≤ 3
∴ cos-1 (x - 2) का डोमेन [1, 3] है।
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