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BITSAT2023MathematicsFunctionsActual

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

Options

  1. A[-1,- 1 2 ] [ 1 2 , 1 ]
  2. B[-1,1]
  3. C(- ,- 1 2 ] [ 1 2 ,+ )
  4. D[ 1 2 , 1 ]

Correct answer

D. [ 1 2 , 1 ]

Step-by-step solution

For f(x) to be defined, we must have x- 1-x^2 0 or x 1-x^2 >0 or x^2 1-x^2 or x^2 1 2 . Now, x^2 1 2 (x- 1 2 ) (x+ 1 2 ) 0 x - 1 2 or x 1 2 Also, 1-x^2 0 or x^2 1 . Also, x^2 1 (x-1)(x+1) 0 -1 x 1 Thus, x>0, x^2 1 2 and x^2 1 x [ 1 2 , 1 ]

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