Question
Download Solution PDFयदि f(x) = 4x + 1 और g(x) = kx + 2 इस प्रकार है कि fog(x) = gof(x) है, तो k का मान क्या है ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFव्याख्या:
दिया गया है: f(x) = 4x + 1 और g(x) = kx + 2 जैसा कि fog(x) = gof(x)
fog(x) = f(g(x)) = 4g(x) + 1
⇒ fog(x) = 4(kx + 2) + 1 = 4kx + 9 __-(i)
और gof(x) = g(f(x)) = kf(x) + 2
⇒ gof(x) = k(4x + 1) + 2 = 4kx + k + 2 __(ii)
चूँकि fog(x) = gof(x), इसलिए (i) और (ii) को बराबर रखने पर,
⇒ 4kx + 9 = 4kx + k + 2
⇒ 9 = k + 2
⇒ k = 7
∴ सही विकल्प (1) है।
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.