JEE Main202131 Aug 2021Evening ShiftMathematicsFunctionsActual
The domain of the function, f x = sin - 1 3 x 2 + x - 1 ( x - 1 ) 2 + cos - 1 x - 1 x + 1 is:
Options
- A0 ,   1 2
- B0 ,   1 4
- C1 4 ,   1 2 ∪ 0
- D- 2 ,   0 ∪ 1 4 ,   1 2
Correct answer
C. 1 4 ,   1 2 ∪ 0
Step-by-step solution
The domain of the function f x = sin - 1 3 x 2 + x - 1 ( x - 1 ) 2 + cos - 1 x - 1 x + 1 For, cos - 1 x - 1 x + 1 - 1 ≤ x - 1 x + 1 ≤ 1 ⇒ - 1 ≤ 1 - 2 x + 1 ≤ 1 ⇒ - 2 ≤ - 2 x + 1 ≤ 0 ⇒ 0 ≤ 1 x + 1 ≤ 1 ⇒ x + 1 ∈ [ 1 , ∞ ) ⇒ x ∈ [ 0 , ∞ )   . . . . i For, sin - 1 3 x 2 + x - 1 ( x - 1 ) 2 - 1 ≤ 3 x 2 + x - 1 x - 1 2 ≤ 1   ⇒ - x - 1 2 ≤ 3 x 2 + x - 1 ≤ x - 1 2 ,   x ≠