Question
Download Solution PDFWhat is the range of the function f(x) = 1 - sinx defined on entire real line?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The range of a function is the set of all its outputs.
Example:
Let us consider the function f: A→ B,
where f(x) = 2x and A and B = {set of natural numbers}.
Here we say A is the domain and B is the co-domain.
The set of ƒ images of all the elements of A is known as the range of ƒ.
Calculation:
f(x) = 1 - sinx
Here the domain of f(x) is (-∞, ∞)
At this domain, the range of sinx is [-1, 1]
Range of f(x) = 1 - sin2x = 1 - [-1, 1]
⇒ f(x) = [0 , 2]
∴ Range of f(x) is [0 , 2].
Last updated on Jul 7, 2025
->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.
->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.
-> 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.