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JEE Main202624 January 2026Evening ShiftMathematicsInverse Trigonometric FunctionsActual

If the domain of the function f(x)= ⁻¹ ( 1 x²-2 x-2 ) , is (- , ] [ , ] [ , ) , then + + + is equal to

Options

  1. A2
  2. B3
  3. C4
  4. D5

Correct 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 .

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