BITSAT2020MathematicsFunctionsActual
The domain of the function f(x)= x- 1-x² is
Options
- A[-1,- 1 2 ] [ 1 2 , 1 ]
- B[-1,1]
- C(- ,- 1 2 ] [ 1 2 ,+ )
- 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-x² 0 or x 1-x² >0 x² 1-x² or x² 1 2 Also, 1-x² 0 or x² 1 . Now, x² 1 2 (x- 1 2 ) (x+ 1 2 ) 0 x - 1 2 or x 1 2 Also, x² 1 (x-1)(x+1) 0 -1 x 1 Thus, x>0, x² 1 2 and x² 1 x [ 1 2 , 1 ]