Question
Download Solution PDFफलन \(f(x) =\sqrt{1 - (x-1)^2} \ \) का प्रांंत क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
फलन y = √f(x), f(x) > 0 के लिए परिभाषित है।
यदि (x - a)(x - b) ≤ 0 है, तो ⇒ x ∈ [a, b] है।
गणना:
दिया गया है कि, \(f(x) =\sqrt{1 - (x-1)^2} \ \)
एक फलन को परिभाषित करने के लिए,
1 - (x - 1)2 ≥ 0
⇒ (x - 1)2 - 1 ≤ 0
चूँकि, (a - b)2 = a2 - 2ab + b2 है,
⇒ x2 + 1 - 2x - 1 ≤ 0
⇒ x2 - 2x ≤ 0
⇒ x(x - 2) ≤ 0
∴ x ∈ [0, 2]
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.