Question
The domain of the function f(x)= x- 1-x^2 is
BITSAT
Mathematics
Functions
2023
BITSAT 2023 (Memory Based Paper 2)
BITSAT Mathematics Question (2023) — Solution
Options
- A. [-1,- 1 2 ] [ 1 2 , 1 ]
- B. [-1,1]
- C. (- ,- 1 2 ] [ 1 2 ,+ )
- D. [ 1 2 , 1 ]
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 ]
Related: Mathematics — Functions · All PYQ Banks