Question
If the domain of the function f(x)= ^ -1 ( 1 x^ 2 -2 x-2 ), is (- , ] [ , ] [ , ), then + + + is equal to
JEE Main
Mathematics
Inverse Trigonometric Functions
2026
JEE Main 2026 (24 January Shift 2)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 2
- B. 3
- C. 4
- D. 5
Answer
C. 4
Step-by-step solution
For ^ -1 ( 1 x^2-2x-2 ) to be defined, we need | 1 x^2-2x-2 | 1, i.e., |x^2-2x-2| 1. Case 1: x^2-2x-2 1 x^2-2x-3 0 (x-3)(x+1) 0 x -1 or x 3. Case 2: x^2-2x-2 -1 x^2-2x-1 0 (x-1)^2 2 1- 2 x 1+ 2 . Domain = (- , -1] [1- 2 , 1+ 2 ] [3, ). So = -1,\ = 1- 2 ,\ = 1+ 2 ,\ = 3. + + + = -1 + 1 - 2 + 1 + 2 + 3 = 4.
Related: Mathematics — Inverse Trigonometric Functions · All PYQ Banks