Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NDA 2020 · Mathematics · Inverse Trigonometric Functions

What is the domain of the function f(x)= ^ -1 (x-2) ?

What is the domain of the function f(x)=cos⁡−1(x−2)f(x)=\cos ^{-1}(x-2) ?

Options

  1. A[−1,1][-1,1]
  2. B[1,3][1,3]
  3. C[0,5][0,5]
  4. D[−2,1][-2,1]

Correct answer

B. [1,3][1,3]

Step-by-step solution

f(x)=cos⁡−1(x−2)f(x)=\cos ^{-1}(x-2) Domain of cos⁡−1(x−2)=[−1,1]\cos ^{-1}(x-2)=[-1,1]∴−1≤x−2≤1−1+2≤x≤1+21≤x≤3∴ Domain =[1,3]\begin{aligned} & \therefore-1 \leq x-2 \leq 1 \\ & -1+2 \leq x \leq 1+2 \\ & 1 \leq x \leq 3 \\ & \therefore \text{ Domain }=[1,3] \end{aligned}$$
Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

Consider the following in respect of inverse circular functions : I. ^ -1 (-x)=- ^ -1 x… NDA 2026What is [2 ^ -1 (1)/(2)-(π)/(4)] equal to ? NDA 2026If ^ -1 k + ^ -1 (1)/(2) = (π)/(4) , then what is the value of k ? NDA 2025What is the value of [(1)/(2) ^ -1 ( 2 3 )]? NDA 2025Consider the following for the two (02) items that follow: Let y = ^ -1 (x - (4x^3)/(27))… NDA 2025If k is a root of x^2 - 4x + 1 = 0 , then what is ^ -1 k + ^ -1 (1)/(k) equal to? NDA 2025What is ^ -1 9 + cosec^ -1 ( 41 4 ) equal to? NDA 2025What is ^2 ( ^ -1 2)+ ^2 (cosec^ -1 3) equal to? NDA 2024If ^ -1 x= ^ -1 x , then which one of the following is correct? NDA 2024What is 15+ ^2((π)/(4)-2 ^ -1 3) equal to? NDA 2024If 4 ^ -1 x+ ^ -1 x=π , then what is ^ -1 x+4 ^ -1 x equal to? NDA 2024What is ^ -1 ((a)/(b))- ^ -1 ((a-b)/(a+b))equal to? NDA 2024What is 2 ((1)/(2) ^ -1 5 3 )equal to? NDA 2023If ^ -1 p-cosec^ -1 q=0 , where p > 0, q > 0 ; then what is the value of ^ -2 + ^ -2 ? NDA 2023What is 1+ ^2 ( ^ -1 ( 3 17 ))equal to? NDA 2023What is ^ -1 (cosec^ -1 2) equal to? NDA 2022 Full Inverse Trigonometric Functions list Inverse Trigonometric Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs