NTA Abhyas JEE Main2020MathematicsFunctionsPractice

The domain of the function f x = x - 1 - x 2 4 is

Options

A- 1 , - 1 2 ∪ 1 2 , 1
B- 1 , 1
C- ∞ , - 1 2 ∪ 1 2 , ∞
D1 2 , 1

Correct answer

D. 1 2 , 1

Step-by-step solution

f x = x - 1 - x 2 4 For f x to be real x - 1 - x 2 ≥ 0 and 1 - x 2 ≥ 0 ⇒ 2 x 2 - 1 ≥ 0 and x 2 - 1 ≤ 0 ⇒ x + 1 2 x - 1 2 ≥ 0 and x + 1 x - 1 ≤ 0 ⇒ x ≤ - 1 2 or x ≥ 1 2 and x ∈ - 1 , 1 When x ∈ - 1 , - 1 2 , then x - 1 - x 2 is negative Hence, the required domain is 1 2 , 1

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