Question
Download Solution PDFफलन f(x) = sin-1 (x + 1) का डोमेन क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFअवधारणा:
डोमेन प्रतिलोम त्रिकोणमितीय फलनों की सीमा है।
| फलन | डोमेन | मुख्य मान की सीमा |
| sin-1 x | [-1 1] | [-π/2, π/2] |
| cos-1 x | [-1 1] | [0, π] |
| cosec-1 x | R - (-1, 1) | [-π/2, π/2] - {0} |
| sec-1 x | R - (-1, 1) | [0, π] - {π/2} |
| tan-1 x | R | (-π/2, π/2) |
| cot-1 x | R | (0, π) |
गणना:
दिया गया है: f(x) = sin-1 (x + 1)
⇒ y = sin-1 (x + 1)
दिए गए फलन को sin y = x + 1 के रूप में लिखा जा सकता है
हम जानते हैं कि sin y एक ऐसा फलन है जो -1 और 1 के बीच दोलन करता है
अर्थात यह अंतराल [-1, 1] में मान के रूप में सभी वास्तविक संख्याओं को ले सकता है
तो, -1 ≤ sin y ≤ 1
⇒ -1 ≤ x + 1 ≤ 1
⇒ -1 - 1 ≤ x + 1 - 1 ≤ 1 - 1
⇒ -2 ≤ x ≤ 0
∴ x ∈ [-2, 0]
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