The domain of the function f : R → R defined by \(\rm \sqrt {x^2 \ - \ x - 110}\) is.

  1. (- ∞, - 10] ∪ [11, ∞)
  2. (- ∞, 11] ∪ [- 10, ∞)
  3. (- ∞, 10] ∪ [- 11, ∞)
  4. (- ∞,  10] ∪ [11, ∞)

Answer (Detailed Solution Below)

Option 1 : (- ∞, - 10] ∪ [11, ∞)
Free
Agniveer Navy SSR Full Test - 01
4.1 K Users
100 Questions 100 Marks 60 Mins

Detailed Solution

Download Solution PDF

Concept:

The domain of a function is the complete set of possible values of the independent variable.

To find domain of √f(x), set f(x) ≥ o

Calculations:

Given: the function f : R → R defined by \(\rm \sqrt {x^2 \ - \ x - 110}\)

We know that the domain of a function is the complete set of possible values of the independent variable.

To find the domain

= x2 - x - 110 ≥ 0

= x2 - 11x + 10x - 110 ≥ 0

= x(x - 11) + 10(x - 11) ≥ 0

= (x + 10)(x - 11) ≥ 0

= x ≤ - 10 or x ≥ 11

= x ∈ (- ∞, - 10] ∪ [11, ∞)

Hence, the domain of the function f : R → R defined by f(x) = \(\rm \sqrt {x^2 \ - \ x - 110}\) is (- ∞, - 10] ∪ [11, ∞)

Latest Indian Navy Agniveer SSR Updates

Last updated on May 31, 2025

-> The Indian Navy SSR Agniveeer Merit List will be released soon on the official website.

-> The Indian Navy Agniveer SSR CBT Exam was conducted from 25th to 26th May 2025.

->The application window was open from 29th March 2025 to 16th April 2025.  

-> The Indian Navy SSR Agniveer Application Link is active on the official website of the Indian Navy.

.->Only unmarried males and females can apply for Indian Navy SSR Recruitment 2025.

-> The selection process includes a Computer Based Test, Written Exam, Physical Fitness Test (PFT), and  Medical Examination.

->Candidates Qualified in 10+2 with Mathematics & Physics from a recognized Board with a minimum 50% marks in aggregate can apply for the vacancy.

-> With a salary of Rs. 30,000, it is a golden opportunity for defence job seekers.

-> Candidates must go through the Indian Navy SSR Agniveer Previous Year Papers and Agniveer Navy SSR mock tests to practice a variety of questions for the exam.

Get Free Access Now
Hot Links: rummy teen patti teen patti comfun card online teen patti master gold